Mixed refrigerant Joule-Thomson (MRJT) cryocoolers can produce cryogenic temperatures with high efficiency and low operating pressures. As compared to the high system pressures of around 150–200 bar with nitrogen, the operational pressures with non-azeotropic mixtures (eg, nitrogen-hydrocarbons) come down to 10–25 bar. With mixtures, the heat transfer in the recuperative heat exchanger takes place in the two-phase region. The simultaneous boiling and condensation of the cold and hot gas streams lead to higher heat transfer coefficients as compared to single phase heat exchange. The two-phase heat transfer in the recuperative heat exchanger drastically affects the performance of a MRJT cryocooler. In this work, a previously reported numerical model for a simple tube-in-tube heat exchanger is extended to a multi tubes-in-tube heat exchanger with a transient formulation. Additionally, the JT expansion process is also considered to simulate the cooling process of the heat exchanger from ambient temperature conditions. A tubes-in-tube heat exchanger offers more heat transfer area per unit volume resulting in a compact design. Also, the division of flow in multiple tubes reduces the pressure drop in the heat exchanger. Simulations with different mixtures of nitrogen-hydrocarbons are carried out and the numerical results are compared with the experimental data.