"Sound propagation and the initial value problem in kinetic theory are investigated. Linearized forms of certain kinetic models suggested by Gross and Jackson employed. The most general model contains three relaxation times and is capable of producing Euler, Navier-Strokes, Burnett and thirteen moments equations for smooth phenomena. A study of dispersion relations is made and some novel features are uncovered. One finds that kinetic models are unable to describe phenomena of higher than a certain wave number, the latter depending on the model chosen. It compensates for this by introducing an interesting but unphysical dispersion picture for high wave numbers. It is further suggested by one of the models that the phase speed of sound waves achieves a maximum value. Existence, uniqueness, and boundedness of solutions of the initial value problem are shown for any model equations. It is further shown that asymptotically the solutions become hydrodynamical."