In the underlay cognitive radio networks, this paper defines the joint channel and power allocation problem, which aims to optimise the max-total and max-min throughputs of secondary users (SUs), with the constraints of interference on primary receivers. For the max-total problem, we formulate the problem as a bipartite matching and derive a maximum weighted matching-based sum throughput maximisation algorithm (STMA) to solve this problem. For the max-min problem, on the basis of the optimal relay assignment (ORA) algorithm, we derive a polynomial time optimal channel assignment algorithm (OCAA) to iteratively assign channels to each SU pair under the power constraint. Simulation results demonstrate the effectiveness of our algorithms when compared with random method.