In cognitive radio networks, there are two categories of networks on different channels: primary networks, which have high-priority access, and secondary networks, which have low-priority access. We develop an auction-based framework that allows networks to bid for primary and secondary access based on their utilities and traffic demands. The bids are used to solve the access allocation problem, which is that of selecting the primary and secondary networks on each channel either to maximize the auctioneer’s revenue or to maximize the social welfare of the bidding networks, while enforcing incentive compatibility. We first consider the case when the bids of a network depend on which other networks it will share channels with. When there is only one secondary network on each channel, we design an optimal polynomial- time algorithm for the access allocation problem based on reduction to a maximum matching problem in weighted graphs. When there can be two or more secondary networks on a channel, we show that the optimal access allocation problem is NP-complete. Next, we consider the case when the bids of a network are independent of which other networks it will share channels with. We design a polynomial-time dynamic programming algorithm to optimally solve the access allocation problem when the number of possible cardinalities of the set of secondary networks on a channel is upper-bounded. Finally, we design a polynomial-time algorithm that approximates the access allocation problem within a factor of 2 when the above upper bound does not exist.