Iran, Sudan, Venezuela, Syria, deemed to be nuclear threats, insurgent havens or human rights violators by the US, are on the Asian giants' list.
The most recent US concerns have focused on China's bid for Unocal Corp, America's ninth largest oil company.
US congressmen, senators and former CIA director James Woolsey have described it as a threat to US national security.
But less high-profile manoeuvres by the two Asian countries are also raising questions.
Besides their involvement in energy projects worth billions of dollars in countries the US views with concern, India and China also have bought into Russia's oil and gas sector.
And Beijing, with Moscow's apparent blessing, is reaching out to energy-rich former Soviet republics in Central Asia where the US has military outposts.
As their reach grows, China and India are receiving increased attention in Washington.
US President George Bush this week said America's relationship with China was "a good relationship, but it's a complex relationship".
Bush also feted Indian Prime Minister Manmohan Singh at the White House in clear recognition of his country's growing significance.
Bush: US relations with China
good, but complex
The all-out energy offensive by the two Asian powers was documented this year by the National Intelligence Council, the US government think-thank which advises the CIA and senior US policy-makers.
"The likely emergence of China and India as new major global players ... will transform the geopolitical landscape," said the report titled Mapping the Global Future.
"In the same way that commentators refer to the 1900s as the 'American Century', the early 21st century may be seen as the time when some in the developing world, led by India and China, come into their own."
The report also says energy demand to 2020, especially by India and China, "will have substantial impacts on geopolitical relations".
In Asia's former Soviet republics, such moves threaten to hurt US interests by skewing alliances in a key part of the world on the doorstep of the oil-rich Caspian basin and also close to Iraq and Afghanistan.
The need for a US military toehold - established during the Afghanistan offensive - is already being questioned by the governments of Uzbekistan and Kyrgyzstan.
Kyrgyzstan's Kurmanbek Bakiyev
is to review US military presence
The Uzbek Foreign Ministry last month said that other than for overthrowing Afghanistan's Taliban regime, "any other prospects for a US military presence ... were not considered by the Uzbek side".
And a week ago, Kyrgyzstan President Kurmanek Bakiyev said it was time to "begin discussing the necessity of the US military forces' presence".
The Shanghai Cooperation Organisation, a regional alliance led by China and Russia, this month called on the US to set a date for withdrawing forces from the two former Soviet republics.
General Richard Myers, chairman of the US Joint Chiefs of Staff, called it an attempt to "bully" the two US allies - a charge Moscow sharply rejected.
Strategic manoeuvring has always been a part of world rivalries and most nations are not that choosy - Saudi Arabia, the world's largest oil producer, remains crucial to Washington despite its human rights record, for example.
But the imperative of making friends with energy-rich nations has grown over the past two years as oil prices rise and consumption grows.
Much of the oil - a third of the world output - still is pumped by the Vienna-based Organisation of Petroleum Exporting Countries (Opec), with Saudi Arabia as its top producer.
But billions of barrels of the world's reserves are in countries hostile to the US such as Iran, Opec's second largest oil producer, where US sanctions have locked out American oil companies. Billions more are in countries and regions with uncertain loyalties.
Billions of barrels of oil reserves
are in areas hostile to the US
These countries "are a magnet for oil-hungry countries", says Michael Klare, author of Blood and Oil: The Dangers and Consequences of America's Growing Petroleum Dependency.
Chinese oil demand now is second only to the US and within 20 years is it is expected to increase to 21 million barrels a day. That is what the US consumes now - and most of it will be imported.
India's oil consumption over the same period is expected to double to a daily 5.3 million barrels - also mostly imported.
Klare says China's worries about American dominance in the Arabian Gulf, and the Straits of Hormuz through which oil tankers pass, have hastened its scramble for oil rights elsewhere.
"Right now, they get most of their oil from the ... Gulf countries but they are fearful that if the US closes the Straits of Hormuz, then China would be starved of oil."
US in Iraq
Beijing is also casting a wider oil net because the US presence in Iraq - thought to have the world's second-largest oil reserves - has derailed Chinese attempts to establish a toehold there.
Chinese and Indian investments in countries and regions of US concern include:
• A 50% Chinese stake in the sprawling Yadavaran oilfields of Iran, which the US accuses of trying to make nuclear weapons. The Chinese last year also signed deals worth an estimated $70 billion for 250 million tonnes of Iranian liquefied natural gas.
"In the same way that commentators refer to the 1900s as the 'American Century', the early 21st century may be seen as the time when some in the developing world, led by India and China, come into their own"
National Intelligence Council,
US government think-thank
• Majority Chinese control in the consortium dominating the oil industry of Sudan, whose government is accused of human rights abuses linked to massacres in the Darfur conflict.
• Chinese ownership of 60% of a major Kazakhstan oil and gas enterprise, and plans to build a pipeline for Kazakh crude into China.
• India's multibillion-dollar project to pipe in Iranian gas via Pakistan - a plan criticised this month by US Secretary of State Condoleezza Rice.
• Billion-dollar investments by India's main oil and gas enterprise in far-flung projects that include Australia, Russia, Iraq, Syria, Libya, Oman, Qatar, Ivory Coast and Vietnam. India has also signed a pipeline deal with gas-rich Myanmar's military government.
• Chinese and Indian interest in Venezuela, the fourth largest US oil supplier, whose president, Hugo Chavez, is a fierce critic of US foreign policy. Chavez is trying to rewrite concessions to US oil companies and has invited China and India to participate in oil exploration.
Both Beijing and New Delhi deny that their efforts constitute a threat to the United States.
Alluding to concerns about Iran, the Chinese Foreign Ministry said "China's development of friendly relations with another country ... won't harm any other country's interests".
It said Beijing was "devoted to developing constructive and cooperative relations with the United States".
And Sanjay Baru, media adviser to India's Singh, said the pipeline was nothing more than a "bilateral issue between ... India and Iran".
Still, such alliances have already resulted in some US setbacks.
Washington is believed to have used its influence with Panama in past years to reduce Chinese access to the Panama Canal.
But China last year signed a deal with Venezuela and neighbouring Colombia for a pipeline to bypass the Panama Canal and ship Venezuelan oil directly to Colombia's Pacific outlets for loading onto Chinese tankers.
The US is thought to have blocked
China's access to Panama Canal
Iran, whose nuclear ambitions are among Washington's greatest security concerns, also is reaping benefits beyond the cash and energy-related expertise provided by China and India.
Chinese sales of anti-ship missiles and other military hardware to Iran have been documented by US authorities and international non-governmental agencies. They have also drawn repeated US sanctions - most recently last year against eight Chinese companies accused of selling missile technology to Tehran.
China has hinted it would block any US-led attempt for UN Security Council sanctions on Iran over the nuclear issue, saying it "does not support referring the Iranian nuclear question to the Security Council".
Gary Sick, a member of the National Security Council under former president Jimmy Carter, said sanctions on Iran would in effect embargo Iranian oil.