This paper investigates the cooperative multihop cognitive relay networks (CRNs) under a novel two-dimensional spatial-temporal opportunity model, in which free opportunity and sharing opportunity are defined to enhance the spectrum efficiency. Correspondingly, a joint spatial-temporal access scheme (JSTAS) is proposed to realize successive spectrum access for continuous data transmission. The multihop CRNs with fixed relaying employ decode-and-forward with and without signal-to-noise ratio selection, which are named as SDF and DF, respectively. Then, considering the interference constraints from multiple primary receivers, the interference of one primary transmitter and the maximum transmit powers of cognitive users, we study the outage performance of multihop CRNs with JSTAS over Nakagami-m fading. To comprehensively evaluate JSTAS, we further present the pure spatial access scheme (SAS) and the pure temporal access scheme (TAS) under the spatial-temporal opportunity model, and calculate their average network outage probabilities. Simulation results demonstrate that SDF outperforms DF, while JSTAS outperforms SAS and TAS under all considered scenarios.