In a two-particle interferometer, one can study the variation of both single- and joint-detection probabilities as functions of the phase shifts of the beams. By combining the usual definition for one-particle fringe visibility ${\mathit{v}}_{\mathit{i}}$ (i=1,2) with a reasonable proposed definition for two-particle fringe visibility ${\mathit{v}}_{12}$, we show that ${\mathit{v}}_{\mathit{i}}^{2}$+${\mathit{v}}_{12}^{2}$\ensuremath{\le}1 or, equivalently, ${\mathit{v}}_{\mathit{i}}$${\mathit{v}}_{12}$\ensuremath{\le}1/2. Some extensions are discussed.