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Alteative versions of the ZM model are extended to asymmetric nuclear matter by including p meson degree of freedom in the Lagrangian. The extended models are then used to study the thermodynamical properties of asymmetric nuclear matter at finite temperature. The critical temperature for a liquid-gas phase transition in nuclear matter and its dependence on asymmetry parameter are calculated. The limiting temperature Tlim, which reflects Coulomb instability of hot nuclei, is studied.The calculated results are compared with that given by the original ZM model.