There are two equivalent formulations of classical nonlinear response theory for constant external fields, the Transient Time-Correlation Function (TTCP) theory and the Kawasaki distribution function approach. The generalisation of these two formalisms to time- dependent fields has been hindered by the fact that a crucial step in their derivation relies on the property that the equations of motion do not contain any explicit time dependence. The concept of an extending the dimension of phase space so that the resulting equations of motion become autonomous provides a means of avoiding this problem and allows the generalisation of both formulations to treat the nonlinear response of systems to time dependent external fields. These generalisations provide the only time-dependent nonlinear response theories which have been successfully applied to computer simulations. The usefulness and efficiency of the both methods is shown in simulations of some simple systems.