The structures of positively and negatively charged clusters of sulfuric acid with ammonia and/or dimethylamine ((CH(3))(2)NH or DMA) are investigated using a combination of Monte Carlo configuration sampling, semiempirical calculations, and density functional theory (DFT) calculations. Positively charged clusters of the formula [(NH(4)(+))(x)(HSO(4)(-))(y)](+), where x = y + 1, are studied for 1 <= y <= 10. These clusters exhibit strong cation-anion interactions, with no contribution to the hydrogen-bonding network from the bisulfate ion protons. A similar hydrogen-bonding network is found for the [(DMAH(+))(3)(HSO(4)(-))(4)](-) cluster. Negatively charged clusters derived from the reaction of DMA with [(H(2)SO(4))(3)(NH(4)(+))(HSO(4)(-))(2)](-) are also studied, up to the fully reacted cluster [(DMAH(+))(4)(HSO(4)(-))(5)](-). These clusters exhibit anion-anion and ion-molecule interactions in addition to cation-anion interactions. While the hydrogen-bonding network is extensive for both positively and negatively charged clusters, the binding energies of ions and molecules in these clusters are determined mostly by electrostatic interactions. The thermodynamics of amine substitution is explored and compared to experimental thermodynamic and kinetic data. Ammonia binds more strongly than DMA to sulfuric acid due to its greater participation in hydrogen bonding and its ability to form a more compact structure that increases electrostatic attraction between oppositely charged ions. However, the greater gas-phase basicity of DMA is sufficient to overcome the stronger binding of ammonia, making substitution of DMA for ammonia thermodynamically favorable. For small clusters of both polarities, substitutions of surface ammonium ions are facile. As the cluster size increases, an ammonium ion becomes encapsulated in the center of the cluster, making it inaccessible to substitution.