By　taking　the　advantage　of　Poisson　events,　the　outcrossing　method　has　been　widely　applied　for　time-dependent　reliability　analysis　considering　continuous　processes.　Generally,　the　outcrossing　method　can　only　obtain　an　upper　bound　of　failure　probability,　which　will　overestimate　the　risk　and　result　in　unnecessary　maintenance　costs.　In　this　study,　a　general　conditional　outcrossing　(GCO)　method　for　time-dependent　reliability　analysis　was　proposed,　which　can　obtain　a　more　accurate　probability　of　failure.　The　conditional　outcrossing　rate　was　defined　as　the　outcrossing　rate　conditioned　on　fixing　the　values　of　time-invariant　random　variables,　which　was　introduced　to　satisfy　the　assumption　of　independent　outcrossing　events.　A　numerical　algorithm　for　the　GCO　method　was　developed　with　the　aid　of　the　Gauss-Legendre　quadrature　and　point　estimate　method.　The　application　of　the　GCO　method　is　demonstrated　by　three　examples,　including　an　implicit　limit　state　function　with　a　finite-element　model　and　non-Gaussian　nonstationary　random　processes.　The　failure　probability　obtained　by　the　GCO　method　was　found　to　be　in　close　agreement　with　that　by　Monte　Carlo　simulation,　which　demonstrates　the　accuracy　of　the　GCO　method.