We report the first observation of anticrossings in solid-state laser spectroscopy. Measurements are performed on the 6105- zero-phonon transition H43(Γ1) D21(Γ1) of Pr3+ in a YA103 crystal at 2°K where both ground- and excited-state anticrossings appear. A perturbation theory of the anticrossing signal is derived from the wave equations of motion for a three-level quantum system subject to a static interaction V between two neighboring levels (1 and 2) while a laser field resonantly excites the inhomogeneously broadened 23 transition. Ground- and excited-state gyromagnetic ratios γi(i=X,Y,Z) and the interactions V are obtained by fitting the observed anticrossings to a diagonalized hyperfine-spin Hamiltonian for Pr3+141 which includes second-order ligand field corrections in terms containing the electron orbital angular momentum. Under certain conditions, one anticrossing signal develops into a strongly modulated oscillation with a period of ∼ 20 G, an unexpected feature which appears to be a nonlinear optical coherence effect. The influence of anticrossing state mixing on optical free-induction-decay observations is also discussed. © 1981 The American Physical Society.