The two banks showed a dip in investment banking income in the latest quarter, but more than made up for that with lower losses on personal and corporate loans as broad economic conditions improved.
HSBC said the amount of money it set aside to cover bad loans had fallen to $7.5bn for the half-year, down $6.4bn from the level a year ago level.
BNP's second-quarter provisions for bad loans halved to $1.88bn, the lowest in two years.
The French bank said this reflected an improving but still challenging macroeconomic environment in its key eurozone markets.
"HSBC and BNP have seen provisions cut in half year-on-year," Francois Chaulet, fund manager at Montsegur Finance Asset Management in Paris, said.
"We are very rapidly seeing big retail banks like BNP and HSBC return to a level of provisions that is very close to what it was before the crisis."
HSBC warned that growth could remain anaemic in various Western countries, although it was bullish on the prospects for emerging markets, even if "some cooling off" in China's economy is possible.
The London-based bank moved its chief executive to Hong Kong earlier this year and is shifting its weight further to Asia.
The prospects of bumper profits for banks in Britain and elsewhere will raise pressure from politicians to force them to lend more and potentially revive talk of an industry tax, after the sector was lifted by the watering down of capital reform.
Lloyds Banking Group and Societe Generale are due to report Wednesday, followed by Barclays on Thursday and Royal Bank of Scotland on Friday.