Multistream heat exchangers (MHEXs) are often used in energy-intensive cryogenic processes. Modeling them within a process optimization formulation has been a challenge due to the needs to accommodate phase changes and ensure temperature approach. In this work, we present a nonlinear model for MHEXs based on a novel single-stage superstructure of two-stream exchangers. Our formulation guarantees a minimum temperature approach for all heat exchanges, estimates heat exchange areas for individual stream matches, requires no prior knowledge of phase changes, uses no Boolean variables, and enables seamless optimization of a process with multiple MHEXs. Furthermore, it facilitates dedicated constant-phase intervals that allow accurate estimation of heat-transfer parameters for various stream matches. We optimize two natural gas liquefaction processes involving MHEXs, and report better solutions than the existing literature. (c) 2017 American Institute of Chemical Engineers AIChE