We analyze simple predator-prey models in stochastic environments by a perturbational approach near bifurcating regimes. We obtain the stationary probability distribution for the radial variable, even when the system is on a limit cycle. The basic technique involves an adaptation of the method of averaging to take account of random fluctuations. The Fokker-Planck equation is used to find the stationary probability distribution of the secular variables. We find: (a) The radius of the limit cycle decreases as noise increases. (b) If noise dispersion is larger than the deterministic radius, no limit cycle exists. Hence, if noise is relatively large, the stationary probability distribution of a small deterministic limit cycle may be.diflicult to differentiate from the distribution of a stable focus. (c) The dispersion of the angular variable increases linearly in time. We give several remarks concerning soft and hard transitions, and the phenomenon of hysteresis. Finally, we discuss the entrainment of frequen...