The effects of vibronic coupling on the electron paramagnetic resonance of transition metal ions that have orbital triplet ground states in alkaline earth halides have been investigated. Spectra have been obtained for two impurity ions, Cr2+ and Cr3+. The Cr2+ ion in CdPg and CaFg occupies a site that has axial symmetry along (lio) axes of the crystal. The Spin Hamiltonian for this ion which has a spin of two in the ground vibronic state is derived and a preliminary determination of some of the Spin Hamiltonian parameters has been made. According to currently held theoretical ideas, these data can be interpreted as a Static Jahn-Teller Effect in which the electronic triplet state couples to a vibrational doublet state and a vibrational triplet state with comparable coupling strengths. The Cr3+ ion in CaFg bas also been studied. It occupies a site that has axial symmetry along (ill) axes of the crystal. This behavior is predicted from a Static Jahn-Teller Effect in which the triplet electronic state couples predominantly to a triply degenerate vibrational mode. The Cr3+ ion has a spin of (3/2) in the ground vibronic state and the Spin Hamiltonian for this ion is derived. The temperature dependence of the data is used to give a rough estimate of the zero field splitting parameter, D, which agrees with the frequency dependence of the effective g-value.