Abstract: Two methods of genetic evolution of linear and non-linear heuristic evaluation functions for the game of checkers and give-away checkers are presented in the paper. The first method is based on the simplistic assumption that a relation ‘close’ to partial order can be defined over the set of evaluation functions. Hence an explicit fitness function is not necessary in this case and direct comparison between heuristics (a tournament) can be used instead. In the other approach a heuristic is developed step-by-step based on the set of training games. First, the end-game positions are considered and then the method gradually moves ‘backwards’ in the game tree up to the starting position and at each step the best fitted specimen from the previous step (previous game tree depth) is used as the heuristic evaluation function in the alpha-beta search for the current step. Experimental results confirm that both approaches lead to quite strong heuristics and give hope that a more sophisticated and more problem-oriented evolutionary process might ultimately provide heuristics of quality comparable to those of commercial programs.