An ab initio theoretical analysis of the rovibronic spectra of the PdH molecule and its heavier isotope PdD is presented. Potential curves of the lowest Lambda S state multiplet (2) Sigma(+), (2) Delta, and (2) Pi are generated in consideration of kinematic relativistic effects in a one-component formalism. We determine the effects of the rotational motion of the nuclei on the vibronic spectra by evaluating matrix elements of a rotational Hamiltonian in the basis of uncoupled vibronic Born-Oppenheimer functions, including the effects of spin-orbit coupling and compare our results to experiment. Moreover, we present predictions for experimentally yet unknown transitions by calculating energy levels, Omega-, and vibrational splittings of-several excited states.