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Hybrid integration of CMOS and nonvolatile memory (NVM) devices has become the foundation for emerging nonvolatile memory-based computing. The primary challenge to validate hybrid memory system with both CMOS and NVM devices is to develop a SPICE-like simulator that can simulate the dynamic behavior accurately and efficiently. Since memristor, spin-transfer-toque magnetic-tunneling-junction (STT-MTJ) and phase-change-memory (PCM) devices are the most promising candidates of next generation of NVM devices, it is under great interest in including these new devices in the standard CMOS design flow. The previous approaches either ignore dynamic effect without consideration of internal states for dynamic behavior, or need complex equivalent circuits to represent those devices. This paper proposes a new modified nodal analysis for NVM devices with identified internal state variables for dynamic behavior. As such, compact SPICE-like implementation can be derived for all three new NVM devices in the design of large-scale memory circuits. As demonstrated by a number of examples on hybrid memory circuits with both CMOS and NVM devices, our newly developed SPICE-like simulator can capture dynamic behaviors of memristor, STT-MTJ and PCM devices, and can also reduce CPU runtime by 20-69 times when compared to the previous equivalent circuit based approaches.