The behavior of the solute velocity and effective macrodispersivity of solute front in the fracture for the transport in a single fracture in the presence of rock matrix diffusion is analyzed using numerical modeling. The study is limited to a constant continuous solute source boundary condition in a single fracture with constant aperture. Analysis is made for linear and nonlinear sorption cases. Expressions are provided for solute velocity and effective macrodispersivity of the solute fronts during asymptotic and preasymptotic stages using spatial moment analyses. The effective retardation factor and dispersivity of solutes in the fracture are found to follow an exponential function with an exponent related to fracture-matrix parameters. © 2006 ASCE.