After buyout firms enjoyed years of raising money at a rapid clip, Apollo Global Management Inc. and Carlyle Group Inc. are sending their strongest signal yet that era is fading.

Apollo, among the most aggressive private equity firms in gathering cash, told investors earlier this year it planned to raise its $25 billion fund in one go by year-end. It has changed the timetable.

Carlyle told investors at a client meeting earlier this month that it gathered about $15 billion so far for its new buyout and growth fund, the people said. That’s less than the $17 billion it anticipated collecting by roughly midyear as it targets raising $22 billion for the flagship fund.

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