A　segmented　two-phase　flow　model　is　developed　to　describe　immiscible　two-phase　flow　in　discrete　fracture　networks;　i.e.,　there　is　an　abrupt　interface　separating　the　two　immiscible　fluids.　The　capillary　pressure　on　the　fluid　material　interface　and　gravity　are　considered.　For　two-phase　flow　in　fracture　networks　it　is　inevitable　to　form　a　mixed　fluid　in　some　fracture　segments.　The　mixed　fluid　is　described　by　a　homogeneous　model,　and　parameter.　gamma　is　introduced　as　a　critical　value　controlling　new　fluid　formation　in　mixed　fluid.　The　governing　equations　for　two-phase　flow　are　solved　with　a　developed　numerical　manifold　method　(NMM)　which　is　verified　using　the　finite　element　and　analytical　methods　with　two　examples.　Two-phase　flow　through　a　single　fracture　intersection　acting　as　one　of　the　basic　elements　for　complex　fracture　networks　is　then　analysed.　Different　inlet　and　outlet　configurations　are　considered　including　one-inlet/two-outlets,　two-inlets/one-outlet　and　one-inlet/multi-outlets.　For　the　second　configuration,　parametric　studies　of　defined　parameter　gamma　and　boundary　conditions　are　carried　out.　In　the　third　configuration,　capillary　pressure　and　gravity　effects　are　discussed.　The　developed　NMM　is　applied　to　the　analysis　of　two-phase　flow　in　a　complicated　fracture　network　showing　that　it　is　an　efficient　method　for　simulating　segmented　two-phase　flow　in　fracture　networks.　Complex　two-phase　flow　characteristics　in　the　fracture　networks　that　cannot　be　addressed　in　continuum　models,　e.g.,　the　change　in　flow　direction　and　transition　from　static　to　flow,　are　also　revealed　and　analysed.