The dynamics of gamma-ray burst (GRB) jets during the afterglow phase is most reliably and accurately modeled using hydrodynamic simulations. All published simulations so far, however, have considered only a uniform external medium, while a stratified external medium is expected around long duration GRB progenitors. Common to all calculations is the initiation of the GRB jet as a conical wedge of half-opening angle theta sub(0) = 0.2 whose radial profile is taken from the self-similar Blandford-McKee solution. The dynamics for stratified external media (k = 1, 2) are broadly similar to those derived for expansion into a uniform external medium (k = 0). The jet half-opening angle is observed to start increasing logarithmically with time (or radius) once the Lorentz factor Gamma drops below theta super(-1) sub(0). The counterjet becomes visible as it becomes sub-relativistic, and for k = 0 this results in a clear bump-like feature in the light curve.