Growth models in which the morphology depends on interactions of the type V(r) = C/r(n) are presented. The growth algorithms are generalizations of DLA. The particles diffuse on a triangular lattice and eventually either stick to the cluster or are lost. Several processes are simulated in this way : in one case only pure sticking is taken into account, in another case evaporation and rearrangement are also allowed to occur. In the former case (with attractive interactions) the clusters exhibit a highly symmetric shape (a sixfold star) whose detailed structure depends on n, C/kT, and time. In the latter case (studied with repulsive dipolar interactions) the tendency to ramification already present in the absence of long-range forces is enhanced. The morphologies resemble the gel clusters growing from the fluid phase in Langmuir monolayers.