Original Title: Dissociation Dynamics Of Diatomic Molecules In Intense FieldsWe study the dynamics of diatomic molecules (dimers) in intense IR and XUV laser fields theoretically and compare the results with measured data in collaboration with different experimental groups worldwide. The first three chapters of the thesis cover the introduction and the background on solving time-independent and time-dependent Schrödinger equation. The numerical results in this thesis are presented in four chapters, three of which are focused on diatomic molecules in IR fields. The last one concentrates on diatomic molecules in XUV pulses. The study of nuclear dynamics of H2 or D2 molecules in IR pulses is given in Chapter 4. First, we investigate the optimal laser parameters for observing field-induced bond softening and bond hardening in D2. Next, the nuclear dynamics of H2 molecular ions in intense laser fields are investigated by analyzing their fragment kinetic-energy release (KER) spectra as a function of the pump-probe delay [tau]. Lastly, the electron localization is studied for long circularly polarized laser pulses. Chapter 5 covers the dissociation dynamics of O2+ in an IR laser field. The fragment KER spectra are analyzed as a function of the pump-probe delay [tau]. Within the Born-Oppenheimer approximation, we calculate ab-initio adiabatic potential-energy curves and their electric dipole couplings, using the quantum chemistry code GAMESS. In Chapter 6, the dissociation dynamics of the noble gas dimer ions He2+, Ne2+, Ar2+, Kr2+, and Xe2+ is investigated in ultrashort pump and probe laser pulses of different wavelengths. We observe a striking "delay gap" in the pump-probe-delay-dependent KER spectrum only if the probe-pulse wavelength exceeds the pump-pulse wavelength. Comparing pump-probe-pulse-delay dependent KER spectra for different noble gas dimer cations, we quantitatively discuss quantum-mechanical versus classical aspects of the nuclear vibrational motion as a function of the nuclear mass. Chapter 7 focuses on diatomic molecules in XUV laser pulses. We trace the femtosecond nuclear-wave-packet dynamics in ionic states of oxygen and nitrogen diatomic molecules by comparing measured kinetic-energy-release spectra with classical and quantum-mechanical simulations. Experiments were done at the free-electron laser in Hamburg (FLASH) using 38-eV XUV-pump--XUV-probe. The summary and outlook of the work is discussed in Chapter 8.