A Monte Carlo procedure is used to examine the structure of equilibrium, colloidal aggregates governed by hard-disk (or hard-sphere) or square-well interparticle interactions, The resulting aggregates consist of a core with a liquid-like topological structure embedded in a fractal, The core extends over three to four particle diameters and its structure and range are determined by the interaction forces, The sheath surrounding the core has a fractal dimension of 1.93, corresponding to that of continuum percolation clusters, in the case of two-dimensional aggregates and a dimension of about 2.9 in the case of three dimensions, The occurrence of liquid-like cores and fractal sheaths is consistent with recently reported results (based on small-angle neutron-scattering studies) on silica dispersions flocculated by weakly charged or uncharged polymers of large molecular weight, The procedure outlined here can be readily extended to other interaction potentials through importance-sampling techniques and can be used for interpreting small-angle radiation-scattering data on colloidal, biological and other dispersions.