This paper presents a novel method for simulation of sampled systems with weakly nonlinear behavior. These systems can be characterized by adding weakly nonlinear terms to the linear state-space equations of the system resulting in an extended state-space model. Perturbation theory is used to split these equations in an ideal linear behavior and a non-ideal small perturbation. The linear equations are solved analytically which reduces simulation time compared to numerical evaluation. The solution of the perturbation equations is approximated by orthogonal polynomials. This methodology not only reduces simulation time compared to traditional numerical simulations, but also deals naturally with clock jitter and the discontinuous behavior of sampled systems. An implementation of the methodology has been used to analyze systems including switched filters and continuous-time ΔΣ modulators.