Results of molecular dynamics simulations for systems with two flexible, oppositely charged polymer chains are presented. The lengths N and interaction strength lambda of the chains are varied. We find that the chains remain separated for small values of lambda. For large interaction strengths, i.e., large Bjerrum lengths, we find glasslike structures and order on the length scale of a few monomer diameters. Between these two limits of the interaction strengths, the chains of various lengths collapse into compact complexes that exhibit self-similar structures. The scaling behavior of the radius of gyration is discussed as a function of chain length and interaction strength. In addition, the local structure of the collapsed systems is analyzed and the dependence of the density of the aggregate on the interaction strength is discussed.