The authors present new filtering algorithms for uncertain-stochastic dynamic systems, which are optimal in the sense of minimax-stochastic criterion. These algorithms allow us to estimate the state vector of dynamic systems given incomplete a priori information about the system characteristics and using observations of the state and input signals. The filtering algorithm is used to construct an optimal two-filter smoothing algorithm for pure uncertain dynamic systems. These algorithms are numerically tested. Results are compared with the results of Kalman filtering and smoothing in the case of complete information about the input signal characteristics.