Speech prediction is extensively based on linear models. However, components generated by nonlinear effects are also contained in speech signals, which is neglected using linear techniques. This paper presents long-term nonlinear predictor based on second-order Volterra filters that is shown to be superior to linear long-term predictor with only a minimal increase in complexity and the number of coefficients. It can be used connected in cascade with short-term linear predictor. The frame/subframe structure is proposed, where each frame is divided into four subframes. Second order Volterra long-term prediction is applied to each subframe separately.