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In this paper we deal with competitive local on-line algorithms for nonpreemptive channel allocation in mobile networks. The signal interferences in a network are modeled using an interference graph G. We prove that the greedy online algorithm is Δ-competitive, where Δ is the maximum degree of G. We employ the "classify and randomly select" paradigm [5], [17], and give a 5-competitive randomized algorithm for the case of planar interference graphs, a 2-competitive randomized algorithm for trees, and a (2c)-competitive randomized algorithm for graphs of arboricity c. We also show that the problem of call control in mobile networks with multiple available frequencies reduces to the problem of call control in mobile networks with a single frequency. Using this reduction, we present on-line algorithms for general networks with a single frequency. We give a local on-line algorithm which is (α(δ + 1 + α)/(½ + α)²)-competitive, where a is the independence number of G, and δ is the average degree of G. The above results hold in the case when the duration of each request is infinite, and the benefit the algorithm gains by accepting each request is equal to one. They are extended to handle requests of arbitrary durations, and arbitrary benefits. [ABSTRACT FROM AUTHOR]