An unusual type of nonresonant absorption signal produced by the ac Stark effect has been observed in a two-level avoided-crossing system. The theory for these anomalous transitions has been developed. The nonresonant signals have been shown to be caused by the perturbation by the oscillating field of the dephasing of the two-level system at the avoided crossing. A series of measurements of these anomalous transitions has been carried out using the avoided-crossing molecular-beam electric-resonance technique. In addition, different types of resonant multiphoton transitions have been investigated. Results are reported for the AE-barrier anticrossing with J = 1 in CH3SiH3. The experimental findings are in good agreement with the theory developed. PACS Nos.: 33.20Bx, 33.80Be, 42.50Hz