In this paper, we focus on two-level nonlinear programming problems, in which there is not coordination between the decision maker at the upper level and the decision maker at the lower level, and propose a computational method through genetic algorithms for obtaining Stackelberg solutions to two-level nonlinear programming problems. From the properties of the two-level programming problems, we devise a computational method with the nested structure based on the genetic algorithms employing floating-point chromosomal representation of individuals for obtaining the Stackelberg solutions. Numerical examples are given to illustrate the proposed method.