Self-adaptation is an essential feature of natural evolution. However, in the context of function optimization, self-adaptation features of evolutionary search algorithms have been explored only with evolution strategy (ES) and evolutionary programming (EP). In this paper, we demonstrate the self-adaptive feature of real-parameter genetic algorithms (GAs) using simulated binary crossover (SBX) operator and without any mutation operator. The connection between the working of self-adaptive ESs and real-parameter GAs with SBX operator is also discussed. Thereafter, the self-adaptive behavior of real-parameter GAs is demonstrated on a number of test problems commonly-used in the ES literature. The remarkable similarity in the working principle of real-parameter GAs and self-adaptive ESs shown in this study suggests the need of emphasizing further studies on self-adaptive GAs.