In this paper, we will investigate the spectrum handoff schemes for the cognitive radio networks. Spectrum handoff occurs when the primary users appear and the secondary users are using this particular primary user's licensed channel. We compare two major types of spectrum handoff schemes. One is the reactive-sensing spectrum handoff, where the target channel for spectrum handoff is selected or sensed only after the spectrum handoff request is made. The other one is the proactive-sensing spectrum handoff, for which the target channel is predetermined. The advantage of the reactive spectrum handoff is the accuracy of the selected target channel, but pay the cost of sensing time. By contrast, the proactive spectrum handoff avoid the sensing time, but the pre-determined target channel may not be available. We will provide a Preemptive Resume Priority M/G/1 queueing network model to analyze in which condition that the reactive- or proactive-sensing spectrum handoff should be used dependent of sensing time.