Two new classes of robust estimates for ARMA models are introduced: estimates based on residual autocovariances (RA estimates), and estimates based on truncated residual autocovariances (TRA estimates). A heuristic derivation of the asymptotic normal distribution is given. We also perform a Monte Carlo study to compare the robustness properties of these estimates with the least squares, M, and GM estimates. In this study we consider observations that correspond to a Gaussian model with additive outliers. The Monte Carlo results show that RA and TRA estimates compare favorably with respect to least squares, M, and GM estimates.