The allegations were made in response to a July 12 lawsuit in which the former executive, Imran Siddiqui, said Apollo and Black tried illegally to undermine his new venture, Caldera Holdings Ltd, and prevent it from competing with their "golden goose," the insurer Athene Holding Ltd.

It is rare for private equity firms to accuse former executives publicly of stealing trade secrets.

Apollo and Siddiqui have had multiple cases against each other, including in arbitration.

In a filing with a New York state court in Manhattan, Apollo and Black said emails uncovered from early 2017 show that Siddiqui was "surreptitiously working" with a more junior Apollo colleague and two former Athene executives, and using confidential information to form a competing company.

The emails are "stark and blatant examples of Siddiqui's betrayal of Apollo and Athene" when he was still a highly paid Apollo partner and should have been loyal, the filing said.

Siddiqui's lawyer Lisa Solbakken said the emails reflect no wrongful conduct, and the new allegations should be rejected.

"Apollo had released Mr. Siddiqui from any and all claims, known or unknown, prior to Feb. 21, 2018," she said in an interview. "The reference to emails in 2017 smacks of desperation."

A hearing on Apollo's and Athene's effort to dismiss Caldera's lawsuit has not been scheduled.

Black, 67, is worth $6.2 billion, according to Forbes magazine.

Athene and Caldera have battled each other for control of American Equity Investment Life Holding Co, an annuities specialist that put itself up for sale in May, the Financial Times has reported.

Apollo created Athene in 2009 to buy insurance assets that were hit hard during the global financial crisis.

Athene has since become a large U.S. annuity provider, with net income nearly doubling last year to $1.45 billion.

Apollo recently owned about 10 percent of Athene and controlled more than one-third of its voting power, according to a regulatory filing.

Siddiqui worked at Goldman Sachs Group Inc and Oak Hill Capital Partners before joining Apollo. Caldera has said he denied possessing confidential Apollo materials.

The case is Caldera Holdings Ltd et al v Apollo Global Management LLC et al, New York State Supreme Court, New York County, No. 652175/2018.

(Reporting by Jonathan Stempel in New York; Editing by Dan Grebler)

By Jonathan Stempel