Credit: Alexandra Wyman/; Charles Eshelman/FilmMagic

Baldwin vs. Costner!

Jury selection began Monday for Stephen Baldwin's lawsuit against Kevin Costner, and both stars appeared in court, CBS News reports.

Baldwin, 46, filed a lawsuit against Costner, 57, in December 2010, claiming the actor cheated him and his friend, Spyridon C. Contogouris, out of their shares of an $18 million deal for BP to buy oil-separating devices after the April 2010 oil spill in the Gulf of Mexico.

The device was developed by Costner's company Ocean Therapy Solutions, and Baldwin says he and Syridon didn't know about the BP deal when they agreed to sell their shares.

The lawsuit claims BP agreed to make an $18 million deposit on a $52 million order for 32 devices.

Baldwin and Contogouris say they are entitled to shares of BP's deposit and are seeking more than $21 million in damages.

In counterclaims, Costner and other defendants also are also seeking damages.