Causality and stability are fundamental concepts for any fluid dynamical theory. In this talk, I will discuss the constraints these concepts imply for the hydrodynamical evolution of high energy simulations. I will present an example of stability analysis which examines the response of a multi-component fluid system to linear perturbations and evaluate the set of conditions under which the equations of motion are hydrodynamically and thermodynamically stable. These conditions become significantly important for the search for the conjectured QCD critical point is being conducted experimentally at large baryon densities where explicit inclusion of finite baryon, strangeness, and electric charge density is required