  We describe how geometrical methods can be applied to a system with
explicitly time-dependent second-class constraints so as to cast it in
Hamiltonian form on its physical phase space. Examples of particular interest
are systems which require time-dependent gauge fixing conditions in order to
reduce them to their physical degrees of freedom. To illustrate our results we
discuss the gauge-fixing of relativistic particles and strings moving in
arbitrary background electromagnetic and antisymmetric tensor fields.
