We　propose　a　quantum　nondemolition　measurement　of　the　photon-number　distribution　for　a　two-mode　cavity　field.　In　the　scheme　two　sequences　of　two-level　atoms　interact　dispersively　with　the　respective　cavity　modes　and　resonantly　with　two　classical　fields,　and　then　are　detected　continually.　The　field　finally　reduces　to　a　two-mode　Fock　state.　The　probability　of　collapsing　to　a　given　Fock　state　is　determined　by　the　initial　photon-number　distribution.　The　scheme　can　be　easily　generalized　to　a　field　with　N　modes.