Twitter, seemingly pulled into the Facebook-Cambridge Analytica controversy, was down a big 10.4%, closing at $31.35. Social-media competitor Snap Inc. lost 2.6% to $16.00.

For its part, Facebook lost another 2.6% on Tuesday -- after a 6.7% drop on Monday.

A report from The New York Times and The Guardian over the weekend alleged that data firm Cambridge Analytica improperly gained access to the data of more than 50 million Facebook users.

Other big media losers included Discovery, down 4.2% to $21.99; Comcast, down 2% to $34.58; Dish Network, falling 2% to $38.81; Charter, losing 1.6% to 327.59; Viacom, down 1.2% to $30.99; and CBS dropping 1% to $50.26. TV station group Tegna declined 3.9% to $11.86.

Alphabet (Google) avoided some of the major declines of its digital media rivals -- slipping just 0.4% to 1,095.80.

Dow Jones Industrials were up 0.5%, or 116 points to 24,727; S&P 500, adding 0.2% to 2,716; and Nasdaq, up 0.3% to 7,364.