The dynamical behavior of H2 in near-infrared, intense laser fields (I gt; 1013 W cm-2 and λ> 700 nm) was discussed on the basis of the results of accurate electronic and nuclear wave packet propagation obtained by the application of the dual transformation method. Using field-following time-dependent (TD) adiabatic states defined as the eigenfunctions of the instantaneous electronic Hamiltonian including the dipole interaction with laser fields, we clarified the dynamics of the bound electron, ionization processes, Coulomb explosion processes, and field-induced molecular vibration of H2. The analyses indicate that the electron dynamics and nuclear (reaction) dynamics of polyatomic molecules in intense fields can be described by using the potential surfaces of TD adiabatic states and the nonadiabatic coupling elements between those states. To obtain the TD adiabatic states of a molecule, one can diagonalize the electronic Hamiltonian including the interaction with the instantaneous laser electric field by ab initio electronic structure calculations. We then present the results of simulation as to how much vibrational energy is acquired by C60(or C60z+) through the interaction with an ultrashort intense pulse ofλ = 1,800 nm. This type of simulation was carried out by incorporating an ab initio classical molecular dynamics method into the framework of the TD adiabatic state approach. The results indicate that large-amplitude vibration with energy of >20 eV is induced in the hg(1) prolate-oblate mode of C60 or C60z+. We found that the acquired vibrational energy is maximized at Tp ~ Tvib/2, where Tp is the pulse length and Tvib is the vibrational period of the hg(1) mode.