Within the cascade approach to the design of state and perturbation observers, an original method for estimating the derivatives of external perturbations that affect a controlled object is proposed. This method is based on virtual dynamic models compiled by the sequential differentiation of some derivatives of the object’s state variables. Observers are constructed as replicas of virtual models. A cascade design procedure for the observers of the derivatives of external perturbations with piecewise linear corrections is developed. In this procedure, the motions separation method in the virtual space of observation errors is implemented. The observer’s variables and also their corrections serve as estimates of the derivatives of external perturbations. They can be used to design combined feedback control and/or to perform current diagnosis of the control process.