A nasty feud that escalated Thursday between Donald Trump and his chief Republican rival over their wives set off a new wave of alarm among establishment Republicans, who fear that the GOP front-runner would drive away female voters in a general-election fight with likely Democratic nominee Hillary Clinton.

Trump’s gender problem flared again this week as he and Sen. Ted Cruz of Texas traded insults while Cruz’s wife, Heidi, became the target of vitriol on social media from Trump and his supporters. At one point, the real estate mogul retweeted an unflattering image contrasting Heidi Cruz’s appearance with his wife, Melania, a retired model.

“The images are worth a thousand words,” read the caption on the photo that Trump retweeted to his 7.2 million followers.

That message and others have prompted an outcry among Republicans and Democrats alike, while Cruz said Thursday that “real men don’t bully women.”

“Our spouses and our children are off-bounds,” Cruz told reporters while campaigning in Dane, Wis. “It is not acceptable for a big, loud New York bully to attack my wife. It is not acceptable for him to make insults, to send nasty tweets.”