  The weak-strong uniqueness for Maxwell--Stefan systems and some generalized
systems is proved. The corresponding parabolic cross-diffusion equations are
considered in a bounded domain with no-flux boundary conditions. The key points
of the proofs are various inequalities for the relative entropy associated to
the systems and the analysis of the spectrum of a quadratic form capturing the
frictional dissipation. The latter task is complicated by the singular nature
of the diffusion matrix. This difficulty is addressed by proving its positive
definiteness on a subspace and using the Bott--Duffin matrix inverse. The
generalized Maxwell--Stefan systems are shown to cover several known
cross-diffusion systems for the description of tumor growth and physical vapor
deposition processes.
