Consider the nondegenerate systems in \(L^ 2:\) \[ (1)\quad A(t,\epsilon)x'=B(t,\epsilon)+f(t,\epsilon) \] where A, B are \(m\times m\)-matrices; \(x,f\in R^ m\), and the degenerate system \[ (2)\quad (\hat A(t)x)'=(\hat A'(t)+\hat B(t))x+\hat f(t). \] The author studies the convergence of the family of the solutions of the system (1) to the solution of the limiting degenerate system.