The paper considers two directions of development of the dynamic-stochastic approach to the construction and use of predictive models. The first direction is related to the uncertainty of the initial state of the simulated process, and the second ‒ to the stochastic nature of model parameter estimates. In the first case, we consider methods for calculating fast-growing perturbations (FGPs) of the initial state of atmospheric dynamics models and a method for using FGPs in optimizing observation systems based on information ordering. An example of determining the zones of dynamic instability of the Northern hemisphere is given. In the second case, a mathematical apparatus for generating perturbations of model parameters in accordance with their probability distribution is proposed. Based on the data of the USSR economic indices, a numerical example of perturbation of parameter estimates and integration of the Volterra model is given.