While detailed descriptions of critical anomalies are well known for thermodynamic variables, the effect of critical fluctuations on microscopic properties is much less well understood. Herein we use the results of molecular dynamics simulation, for the distribution of local densities around a tagged particle in a neat Lennard-Jones fluid, to evaluate the behavior of the self-diffusion coefficient in the critical region (T-r approximate to 1.05; 0.4 < rho (r) < 1.6). We find a weakly anomalous behavior at near critical densities which we attribute to both the broadening of this local-density distribution and the enhancement of mean local density. (C) 2001 American Institute of Physics.