Molecular dynamics computer simulations of solutions of methane in pure and saltwater have been performed, followed by an analysis of the properties of the hydrogen bonds in the solutions. Following the modified hydration-shell hydrogen-bond model of hydrophobic hydration, it is confirmed that in pure water the formation of hydrogen bonds between water molecules in the hydration shell of nonpolar solutes is enthalpically favored and entropically unfavored, with a net positive contribution to the free energy. By contrast, insaltwater, the formation of these same hydrogen bonds in the vicinity of the nonpolar solutes is now enthalpically unfavored and entropically favored, while the contribution to the free energy is even more positive. In pure water, the hydration-shell hydrogen-bonding contribution to the heat capacity of solution is always positive; in saltwater, this contribution is positive at low temperatures but decreases sharply and becomes negative at higher temperatures.