The dynamics of multiphoton excitation of HD+ and H-2(+) in quasi-resonant infrared intense laser fields (I-0 = 1.18 x 10(14) W/cm(2)) is studied by the numerical solution of the time-dependent Schrodinger equations for the systems with explicit treatment of the nuclear vibrations and the electron motion beyond the Born-Oppenheimer approximation. It has been found, in particular, that on the time scale of 400 fs the overall ionization yield is about 40% for HD+, but only about 0.45% for H-2(+). while in accordance with the tunnel (or field) ionization mechanism at least comparable ionization yields could be expected for HD+ and H-2(+). The physical reason for this remarkable difference is that the nuclear motion is excited directly by the strong infrared laser field in HD+, but not in H-2(+) (c) 2005 Elsevier B.V. All rights reserved.