We consider the aggregation processes of model systems consisting of polymer chains and a fluid of Lennard-Jones (L-J) molecules. The neighboring monomers in a polymer chain are connected by springs of five different strengths for five different systems. The bending-angle and torsion-angle potentials of a polymer chain have strength parameters K b and K t , respectively. A small number of randomly chosen “linker sites” along a polymer chain are fluid-attractive, while the other monomers are fluid-repulsive. Using molecular dynamics simulation, we monitor the non-equilibrium aggregation process and analyze its dependence on the strengths of the angle potentials ( K b and K t ) and the monomer–monomer connecting springs. We find that polymer chains tend to aggregate when K b and K t are small enough and the temperature of the monomers is low. A quantitative analysis of the structures reveals the hierarchy in the formation of aggregated clusters. The alignment of local segments of individual chains is followed by the coalescence of these local patches. By removing the fluid and setting the angle potentials to zero, we study the aggregation processes in pure systems. We find the formation of bundle-like aggregated clusters to be robust. Several stages of clustering may prevail when the strength of the springs is increased. To identify the effect of the hindrance caused by the angle potentials, we also simulate systems of mixed chains and fluid, with larger angle potentials. Our analysis suggests that larger angle potentials prevent the aligned local segments from extending spatially and cause the failure of the formation of aggregated clusters. The scenario revealed in this study may be useful for the analysis of protein aggregation in more realistic complex biological systems.