The mutation and cross-over operators are, with selection, the foundation of genetic algorithms. We show in this paper, some possibilities offered by these operators. Having explained the specificity of the most known operators (1-point, p-point and uniform cross-over, classical and deterministic mutation) we introduce new cross­over and mutation operators with a low cost in term of execution time. These operators were designed for Constraint Satisfaction Problem solving, but can be useful in other fields.We also introduce a new diversification operator for graph coloring.