We apply stochastic quantization method to real symmetric matrix models for the second quantization of nonorientable loops in both discretized and continuum levels. The stochastic process defined by the Langevin equation in loop space describes the time evolution of the nonorientable loops defined on nonorientable 2-D surfaces. The corresponding Fokker-Plancr Hamiltonian deduces a nonorientable string field theory at the continuum limit.