Effects of radiation damping on nuclear magnetic resonance (NMR) pulse transient echo and free induction decay (FID) signals in the presence of inhomogeneous magnetic fields are measured and analyzed. An analytical theorem serves as a guide for computer simulations that confirm the experimental results. In comparison to the two-component refocusing of magnetization vectors typically observed as a spin echo in the limit of negligible radiation damping, a two-pulse pi-pi sequence produces an echo where all three components of the magnetization vary and refocus. The analytical. theorem is extended to describe echo properties of various two-pulse and stimulated three-pulse echo sequences. Multiple echoes occur for a class of two-pulse sequences. Multiple rf-pulses interleaved with pulsed magnetic field gradients and the design of multiple pulse sequences for spectroscopic applications are discussed.