Apple (Nasdaq: AAPL), the world's most valuable technology company, kept setting record highs in Tuesday trading. Earlier, its shares hit $674.88, valuing the Cupertino, Calif., company around $630 billion for the first time, more than any other company's prior value.

In early trading, Apple shares eased slightly to $670.33, up $5.18.

No. 2 Exxon Mobil Corp., rose a penny to $87.96, raising the Irving, Tex., energy company's value to $406 billion.