This paper presents new distributed power and admission control algorithms for ad-hoc wireless networks in random channel environments. Previous work in this area has focused on distributed control for ad-hoc networks with fixed channels. We show that the algorithms resulting from such formulations do not accurately capture the dynamics of a time-varying channel. The performance of the network in terms of power consumption and generated interference can be severely degraded when power and admission control algorithms that are designed for deterministic channels are applied to random channels. In particular, some well-known optimality results for deterministic channels no longer hold. In order to address these problems we propose a new criterion for power optimality in ad-hoc wireless networks. We then show that the optimal power allocation for this new criterion can be found through an appropriate stochastic approximation algorithm. We also present a modified version of this algorithm for tracking nonstationary equilibria, which allows us to perform admission control. Ultimately, the iterations of the stochastic approximation algorithms can be decoupled to form fully distributed on-line power and admission control algorithms for ad-hoc wireless networks with time-varying channels.