The clashes happened in eastern and southern Afghanistan, where Taliban and other groups are waging an insurgency against government and foreign forces.
The joint forces clashed with fighters in the Qarabagh district of Ghazni province on Monday, leaving six Taliban dead and eight others wounded, Zia Wali, a spokesman for the provincial governor, said.
There were no casualties among the Afghan and foreign forces, Wali said.
In southwestern Nimroz province, US-led coalition and Afghan troops killed several fighters on Monday during a clash in Khash Rod district, a coalition statement said on Tuesday.
The troops were targeting a fighter involved in the movement of weapons and fighters in the area, it said. They detained 14 other suspected fighters during the raid.
In another incident, US and Afghan troops fought off coordinated insurgent attacks in eastern Afghanistan and called in airstrikes that left a dozen fighters dead and a dozen more wounded, the US military said.
Meanwhile, US marines have pushed into Afghanistan's southern province of Helmand in a major new operation to flush out Taliban fighters.
The Nato-led force described the operation on Tuesday as the most significant in months in the troubled area, which is littered with poppy fields and classified as Taliban territory.
Several hundred marines, many of them veterans of the conflict in Iraq, pushed into the town of Garmser in predawn light.
US commanders say Taliban fighters have been expecting an assault and have been setting up improvised explosive devices in response.
The operation has been called Azada Wosa, which means Be Free in the Pashtu language of southern and eastern Afghanistan.
The marines involved in the new push are based in the neighbouring province of Kandahar.
The assault is the first major task undertaken by the 2,300 soldiers in the 24th Marine Expeditionary Unit, which arrived last month from Camp Lejuene, North Carolina, for a seven-month deployment.
Many of the men in the unit served in 2006 and 2007 in Ramadi, the capital of the Anbar province in western Iraq. The vast region was once the stronghold of al-Qaeda in Iraq.
The marines' mission is the first carried out by US forces this far south in Helmand in years. British troops, who are responsible for Helmand, have faced fierce battles on the north edge of the province.
The largely desert province of Helmand shares a long and porous border with Pakistan, across which Taliban reinforcements are said to cross.