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The isothermal compression tests of C71500 copper-nickel alloy at different temperatures (1073-1273 K) and strain rates (0.01-10 s-1) were carried out on Gleeble-3500 thermo-mechanical simulator. The real stress-strain data were obtained. On the basis of dynamic material model, the power dissipation was established. The peak efficiency of the power dissipation is 57％. At the same time, Prasad's, Murty's and Babu's instability criteria based on Ziegler's expectant rheology theory, and Gegel's and Malas's instability criteria based on Lyaponov's function theory, were used to predict the unstable regions in the processing map. The maximum entropy generation rate and large plastic deformation principle are more in line with the hot deformation process of C71500 alloy, so the accuracy of Prasad's instability criterion is much better. According to the obtained macro-crack and micro-metallographic structure morphologies, the temperature range of 1098-1156 K and the strain rate range of 2.91-10 s-1, and the temperature range of 1171-1273 K and the strain rate range of 0.01-0.33 s-1 are more suitable for the processing area of C71500 alloy. The accuracy of the above conclusions were verified by the forging of materials and the analysis of hot piercing tubes. The significance of this paper is to provide theoretical basis and technological conditions for hot-press processing of C71500 alloy.