In this paper, transient fields inside gyrotropic media are studied by a time domain Green function technique based upon a wave-splitting method. The medium is stratified in one spatial direction and the incident field is a plane electromagnetic pulse of arbitrary waveform at oblique incidence. Green operators are introduced which map the incident field to the internal fields. The relation between the Green operators and the scattering operators used in the invariant imbedding method are discussed. By introducing a complementary medium, a reciprocity relation is derived from which useful relations for the Green operators are obtained.