In this paper, we analyze the delay performance of a point-to-multipoint secondary network (P2M-SN), which is concurrently sharing the spectrum with a point-to-multipoint primary network (P2M-PN). The channel is assumed to be independent but not identically distributed (i.n.i.d.) and has Nakagami-m fading. A constraint on the peak transmit power of the secondary-user transmitter (SU-Tx) is considered, in addition to the peak interference power constraint. The SU-Tx is assumed to be equipped with a buffer and is modeled using the M/G/1 queueing model. The performance of this system is analyzed for two scenarios: 1) P2M-SN does not experience interference from the primary network (denoted by P2M-SN-NI), and 2) P2M-SN does experience interference from the primary network (denoted by P2M-SN-WI). The performance of both P2M-SN-NI and P2M-SN-WI is analyzed in terms of the packet transmission time, and the closed-form cumulative density function (cdf) of the packet transmission time is derived for both scenarios. Furthermore, by utilizing the concept of timeout, an exact closed-form expression for the outage probability of the P2M-SN-NI is obtained. In addition, an accurate approximation for the outage probability of the P2M-SN-WI is also derived. Furthermore, for the P2M-SN-NI, the analytic expressions for the total average waiting time (TAW-time) of packets and the average number of packets waiting in the buffer of the SU-Tx are also derived. Numerical simulations are also performed to validate the derived analytical results. © 1967-2012 IEEE.