Instabilities in astrophysical jets are studied in the nonlinear regime by performing 2D numerical classical gasdynamical calculations. Two kinds of instabilities are studied: (1) those which arise from unsteadiness in output from the central engine feeding the jets, and (2) those which arise from a beam in a turbulent surrounding. An extra power output an order of magnitude higher than is normally delivered by the engine over a time equal to (nozzle length)/(sound velocity at center) causes a nonlinear Kelvin-Helmholtz instability in the jet walls. Constrictions move outwards, but the jet structure is left untouched. A beam in turbulent surroundings produces internal shocks over distances of a few beam widths. If viscosity is present the throughput of material is hampered on time scales of a few beam radius sound travel times.