A cooperative automatic repeat request (ARQ) scheme is proposed for cognitive radio networks with full duplex capability. Its performance is studied for ARQ and hybrid ARQ (HARQ) modes, in terms of data link layer packet error rate (PER) and the primary and secondary throughputs. It is shown that activity of the secondary network during primary's retransmission does not affect primary's performance in ARQ mode, and would even improve it in HARQ mode.