HSBC, the largest bank in Europe, said debts had been written off in the US, Europe and Asia.
Stephen Green, HSBC's chairman, said: "It may be that we have passed, or are about to pass, the bottom of the cycle in the financial markets.
"Nonetheless, the timing, shape and scale of any recovery in the wider economy remains highly uncertain."
In a statement, Barclays said it had made a "good start" to 2009 and was "strongly positioned for the upturn".
Both banks have avoided coming under state control, unlike many of their British rivals.
State-controlled Lloyds and Royal Bank of Scotland, as well as nationalised Northern Rock were devastated by the global financial crisis and were bailed out by the UK government.
All three are due to report results later this week.
Barclays avoided nationalisation in the wake of the credit crunch by courting investment from Abu Dhabi and Qatar in order to bolster its finances.
HSBC and Barclays' profits raise the prospect of large bonuses for its executives which has proved controversial in the current economic climate.
Analysts argue that many bank executives were attracted by short-term profits and the consequent bonuses, damaging their ability to take well-judged business risks, and helping spark the global financial crisis.
The official spokeswoman of Gordon Brown, the UK prime minister, said on Monday that banks needed to ensure that they were chasing long-term stability rather than quick profits.
"We need to make sure that what we see is more credit flowing into businesses and households ... it's important we're looking at long-term stability and not short-term profit," she said.
HSBC shares were up 6.15 per cent in early trading, while Barclays rallied eight per cent, as investors took encouragement from the possibility that the banking sector might be through the worst of the downturn.