This paper discusses two new nuclear magnetic resonance (NMR) techniques for studying ultraslow atomic and molecular motions, and describes their applications to several very dissimilar situations: (1) modulation wave motions in incommensurate insulators, (2) ultraslow atomic motions between chemically inequivalent sites, and (3) restricted diffusion of water molecules in lung. Modulation wave motions and ultraslow atomic diffusion between inequivalent sites have been detected via observations of a Hahn echo decay that is shorter than the Carr-Purcell-Meiboom-Gill decay and is characterized by an exponential dependence on the cube of the echo time. They have also been detected by 2D exchange difference spectroscopy. Restricted diffusion in lung has been studied by measurements of the stimulated echo decay using very large (similar to 1 T/cm) static magnetic field gradients. With this technique the diffusion coefficient D has been measured at very short times, resulting in the detection of the transition from free to restricted diffusion, which in turn allows an estimate to be made of the separation of the restricting boundaries.