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This paper presents a novel method for solving channel assignment problems (CAPs) in hexagonal cellular networks with nonhomogeneous demands in a 2-band buffering system (where channel interference does not extend beyond two cells). The CAP with nonhomogeneous demand is first partitioned into a sequence of smaller subproblems, each of which has a homogeneous demand from a subset of the nodes of the original network. Solution to such a subproblem constitutes an assignment phase, where multiple homogeneous demands are assigned to the nodes corresponding to the subproblem, satisfying all the frequency separation constraints. The whole assignment process for the original network consists of a succession of multiple homogeneous assignments for all the subproblems. Based on this concept, we present a polynomial time approximation algorithm for solving the CAP for cellular networks having nonhomogeneous demands. Our proposed assignment algorithm, when executed on well-known benchmark instances, comes up with an assignment which is always within about 6 percent more than the optimal bandwidth, but requires a very small execution time (less than 5 millisecond on a HPxw8400 workstation). The proposed algorithm is very much suitable for real-life situations, where fast channel assignment is of primary importance, tolerating, however, a marginal deviation (6 percent) from the optimal bandwidth.