Inside the living cell is inherently crowded with proteins and other macromolecules. Thus, it is indispensable to take into account various interactions between the protein and other macromolecules for thorough understanding of protein functions in cellular contexts. Here we focus on the excluded volume interaction imposed on the protein by surrounding macromolecules or "crowding agents." We have presented a theoretical framework for describing equilibrium properties of proteins in crowded solutions [A. R. Kinjo and S. Takada, Phys. Rev. E (to be published)]. In the present paper, we extend the theory to describe nonequilibrium properties of proteins in crowded solutions. Dynamics simulations exhibit qualitatively different morphologies depending on the aggregating conditions, and it was found that macromolecular crowding accelerates the onset of aggregation while stabilizing the native protein in the quasiuniform phase before the onset of aggregation. It is also observed, however, that the aggregation may be kinetically inhibited in highly crowded conditions. The effects of crowding on folding and unfolding of proteins are also examined, and the results suggest that fast folding is an important factor in preventing aggregation of denatured proteins.