AUSTIN, Texas — The Winklevoss twins predicted a “cashless society” by 2025 as they continued their push to popularize the troubled virtual currency bitcoin.

The square-jawed Harvard grads — most famous for their legal battle with former classmate Mark Zuckerberg over the ownership of Facebook — said bitcoin is destined to wipe out the use of cash, credit cards and other fee-based money-transfer services like PayPal.

“Cash is going to be killed,” Tyler Winklevoss told a crowd Monday at SXSW Interactive, the annual tech conference. “It will be nostalgia … You’ll tell your grandkids about the wallet, it was this thing made of leather.”

Cameron Winklevoss chimed in, saying he wasn’t even carrying his wallet at the moment.

“I didn’t want to sit on it for an hour,” he said. “It would hurt my butt.”

Bitcoin has had a bumpy ride over the past year amid hacking scandals and last year’s collapse of Mt. Gox, a Japan-based exchange.

“Personally, we’re not really worried. We’ve not sold a single bitcoin,” Cameron Winklevoss said. “It’s behaving like a technology company. It’s had its ups and downs.”

The duo hope to gain regulatory approval in 2015 for Gemini, a bitcoin exchange, and a bitcoin exchange-traded fund.