A plausible formula derived in a previous paper for the mass ${M}_{n}^{\mathrm{*}}$ of an exciton in an nth bound state of the electron-hole binding potential is extended so as to include the effect of an exciton-hopping (or Heller-Marcus) mechanism upon ${M}_{n}^{\mathrm{*}}$. If ${m}_{e}^{\mathrm{*}}$ and ${m}_{h}^{\mathrm{*}}$ are the electron and hole masses, we find that ${M}_{n}^{\mathrm{*}}$= m $_{e}^{\mathrm{*}}$+${m}_{h}^{\mathrm{*}}$ / 1- ${K}_{n}$ / W + ${m}_{e}^{\mathrm{*}}$+${m}_{h}^{\mathrm{*}}$ / ${M}_{F}^{\mathrm{*}}$ ${H}_{n}$ / ${H}_{F}$, where ${K}_{n}$ and ${H}_{n}$ are, respectively, the kinetic and exciton-hopping energies in the nth bound state; W is one-half the sum of the electron and hole bandwidths, and ${H}_{F}$ is the value taken by ${H}_{n}$ for a Frenkel exciton of finite mass ${M}_{F}^{\mathrm{*}}$. For Wannier excitons, ${K}_{n}$=${H}_{n}$\ensuremath{\simeq}0, so that ${M}_{n}^{\mathrm{*}}$\ensuremath{\simeq}${m}_{e}^{\mathrm{*}}$+${m}_{h}^{\mathrm{*}}$; while for Frenkel excitons, ${K}_{n}$\ensuremath{\simeq}W and ${H}_{n}$\ensuremath{\simeq}${H}_{F}$, so that the mass of the Frenkel exciton ${M}_{F}^{\mathrm{*}}$ is finite as a consequence of the Heller-Marcus mechanism.