<p>The paper proposes a method for constructing new models of stochastic processes whose properties can change significantly at random moments of time, while the process at any moment of time will have an invariant—a function that depends on the state of the process at any moment of time and preserves a constant value with probability 1. The method of constructing systems of Itô stochastic differential equations with Wiener and Poisson perturbations on the basis of invariants and the method of indicator random processes are used for constructing models. The paper presents the following: a model of a random process with transitions between subspaces with preservation of the invariant in each subspace; a model with random switching of regimes and preservation of the invariant in each regime; and a model of a process with invariants and with random time delays. The models presented are supported by examples.</p>