A population «prey-predator» type model with competitions of preys and predators for resources that are different from the prey is considered. Existence and stability of attractors are analyzed, the bifurcation diagram and typical phase portraits are constructed. For the stochastic model, the sensitivity of attractors is analyzed on the basis of the stochastic sensitivity function. Using the confidence domain method (ellipses for equilibria and bands for cycles) stochastic phenomena are studied: transitions of the type «equilibrium —> equilibrium», «cycle —> equilibrium», generation of large-amplitude oscillations and extinction of populations. Probabilistic mechanisms of extinction of populations are studied.