Intramembrane particles (IMPs) of the plasmalemma of mature, synapsing neurons are evenly distributed along the axon shaft. In contrast, IMPs of growing olfactory axons form density gradients: IMP density decreases with increasing distance from the perikarya, with a slope that depends upon IMP size (Small, R., and K. H. Pfenninger, 1984, J. Cell Biol., 98: 1422-1433). These IMP density gradients resemble Gaussian tails, but they are much more accurately described by the equations formulated for diffusion in a system with a moving boundary (a Stefan Problem), using constants that are dependent upon IMP size. The resulting model predicts a shallow, nearly linear IMP density profile at early stages of growth. Later, this profile becomes gradually transformed into a steep nonlinear gradient as axon elongation proceeds. This prediction is borne out by the experimental evidence. The diffusion coefficients calculated from this model range from 0.5 to 1.8 X 10(-7) cm2/s for IMPs between 14.8 and 3.6 nm, respectively. These diffusion coefficients are linearly dependent upon the inverse IMP diameter in accordance with the Stokes-Einstein relationship. The measured viscosity is approximately 7 centipoise. Our findings indicate (a) that most IMPs in growing axons reach distal locations by lateral diffusion in the plasma membrane, (b) that IMPs--or complexes of integral membrane proteins--can diffuse at considerably higher rates than previously reported for iso-concentration systems, and (c) that the laws of diffusion determined for macroscopic systems are applicable to the submicroscopic membrane system.