The nonlinear oblique interaction between a plane tangential discontinuity (TD) and a plane fast magnetogasdynamic shock is treated generally and then applied to the interplanetary TD-bow shock interaction. A number of similarity relations are found for the general problem. For the frequent directional TD's the interaction is strongest if the directional change is 90° and one of the magnetic field vectors is parallel to the shock. Bow shock motions of up to several tens of kilometers per second are induced by these TD's. Tangential discontinuities with density jumps held responsible for geomagnetic sudden impulses lead to a much stronger interaction with the bow shock with nonnegligible strength of the newly generated wave. The oblique interaction requires weaker TD's to produce observed bow shock velocities. It is also shown that complex nonlinear wave patterns very often develop, which have not been predicted in the past in this context.