Advective transport in a heterogeneous two-dimensional aquifer is simulated and quantified by the statistical moments of tracer travel time and transverse displacement. These moments depend on the statistics of the Lagrangian velocity given as a function of space rather than time. A comparison is made with first-order results that appear to be robust for log transmissivity variance at least up to 1. Lagrangian statistics for travel time clearly expose a few essential features of nonlinear transport: nonstationary distribution and the increasing integral scale of the Lagrangian velocity. These reflect the tendency of streamlines to concentrate into relatively few flow paths (''preferential flow'') for increasing log transmissivity variance. Two simple empirical relationships are identified that in combination with first-order results for the flow capture the main features of nonlinear transport. The proposed methodology can readily be generalized for analyzing advective transport under more complex flow conditions and for establishing relatively simple analytical models for estimating solute mass flux in heterogeneous aquifers. ¿ American Geophysical Union 1996