[en] A previously presented path integrals formalism is generalized for cases when the amplitudes have to be considered of histories changing their orientation in time. It is shown that the generalized formalism used for the interaction of a spinless particle with arbitrary electromagnetic fields is not trivial. Speculations are presented indicating that such generalization results in very complex mathematical expressions but that the formalism preserves the basic features thereof. It appears that the formalism may be practically applied only in cases when effects associated with histories which change their orientation in time may be neglected. (Z.J.)