Consider nonlinear autoregressive processes of order 1 defined by the random iteration $$ (1) X_{n + 1} = f(X_n) + epsilon_{n + 1} (n geq 0) $$ where f is real-valued Borel measurable functin on $R^1, {epsilon_n : n geq 1}$ is an i.i.d.sequence whose common distribution F has a non-zero absolutely continuous component with a positive density, $E$mid$epsilon_n$mid$ < infty$</TEX>, and the initial $X_0$ is independent of ${epsilon_n : n > geq 1}$.