Abstract: Generally the mathematical models for population system take no account of the influence of exterior conditions. However, the number of migrating people is increasing rapidly along with the socio-economic development, and the random migration becomes an important perturbative factor to population system. Assuming that the random exterior conditions perturb people's migration, the theories of m-accretive operator and nonlinear semigroup, as the terms included in the nonlinear functional analysis, are applied to deriving the nonlinear equations of evolutional population with random migration perturbation in either definite case or random case, where A represents the m-accretive operator and B the condensing map. Consequently, the theorems proving the existence of local solutions to those equations are obtained.