Genetic algorithms have been successfully applied to various optimization problems belonging to NP-hard problems. The sequential ordering problems(SOP) and the job shop scheduling problems(JSP) are well-known NP-hard problems with strong influence on industrial applications. Both problems share some common properties in that they have some imposed precedence constraints. When genetic algorithms are applied to this kind of problems, it is desirable for genetic operators to be designed to produce chromosomes satisfying the imposed precedence constraints. Several genetic operators applicable to such problems have been proposed. We call such genetic operators precedence-preserving genetic operators. This paper presents three existing precedence-preserving genetic operators: Precedence -Preserving Crossover(PPX), Precedence-preserving Order-based Crossover (POX), and Maximum Partial Order! Arbitrary Insertion (MPO/AI). In addition, it proposes two new operators named Precedence-Preserving Edge Recombination (PPER) and Multiple Selection Precedence-preserving Order-based Crossover (MSPOX) applicable to such problems. It compares the performance of these genetic operators for SOP and JSP in the perspective of their solution quality and execution time.