Various deuterium one- and two-dimensional (2D) NMR techniques are used in the present study to characterize molecular self-diffusive processes in some novel mesophases. Both aligned and powder samples of liquid crystals (LC) are chosen to investigate rotational and/or translational jump diffusions It is demon. strated that rotation of aligned LC samples in a NMR goniometer probe can be helpful in obtaining dynamic and structural information. Both spectral simulations and/or pulse separation (tau) dependences of the quadrupole echo intensity are successfully employed. Deuteron spin-lattice relaxation times and angle dependent spectra are measured in a columnar phase of a monomeric discotogen to illustrate both the fast and intermediate motion regimes. jump diffusions of chiral rodlike molecules in various smectic C* (SmC*) phases and twist grain boundary A* (TGBA*) phase are studied. In the LC 10131M7, the jump rate (or diffusion constant) is determined as a function of temperature in the ferro-, ferri- and antiferro-electric chiral C* phases. 2D deuterium exchange NMR is used to monitor the dynamic processes (self-diffusion) in the ferroelectric SmC* and TGBA* phases. Moreover, packing information of the phase can also be obtained in the two ferrielectric subphases and TGBA* phase, which can be compared With results obtained by X-rays measurements. (C) 2008 Elsevier B.V. All rights reserved.