Effects of high density pumping on relaxation oscillations and mode spectra are investigated in LiNdP <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</inf> O <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</inf> (LNP) lasers. It is shown that high density pumping reduces the spatial population inhomogenuity, which is due to periodic inversion saturation by a first lasing mode in the crystal, and results in spontaneous single longitudinal mode oscillations even at high excitation rates. Physical interpretations are given for single-mode operations on the basis of Auger recombination (annihilation) process for 1.048 and 1.32 μm quantums in LNP lasers. An effective diffusion parameter of excited states is shown in an increase with absorbed pump power density through the Auger process. Observed relaxation oscillation waveforms, which disagreed with the traditional laser dynamic theory, are found to be explained well by the rate equations, including the effective diffusion constant.