The one-dimensional contact region common to shock-tube flows is idealized by the simple model of initial step change in temperature and density at constant pressure. For weak transitions, neglect of pressure effects, and linearization of the conservation equations gives spatially monotonic temperature and density profiles with the contact region thickening as the square root of time. Experimental results are noted from shock-tube studies of two air/air contact regions. Insofar as comparison of theory and experiment is possible, the theory for weak transitions appears reasonable.