In　this　paper,　a　cycle　is　a　graph　in　which　each　vertex　has　even　degree.　A　Fulkerson-cover　of　a　graph　G　is　a　set　of　six　cycles　such　that　each　edge　of　G　is　in　exactly　four　of　the　cycles.　The　well-known　Fulkerson-Conjecture　asserts　that　every　bridgeless　graph　has　a　Fulkerson-cover.　We　prove　that　a　bridgeless　graph　G　has　a　Fulkerson　cover　if　and　only　if　there　are　two　disjoint　sets　E　1　and　E2　of　edges　such　that　E1　∪　E2　is　a　cycle　and　G\Ei　has　a　nowhere-zero　4-flow　for　each　i　=　1,　2.　Using　this,　together　with　a　result　of　Jaeger　related　to　crossing　numbers,　we　verify　the　Fulkerson　Conjecture　for　several　known　classes　of　hypohamiltonian　graphs　in　the　literatures,　including　the　one　based　on　flip-flops　introduced　by　Chvátal.　©　2015　Elsevier　B.V.　All　rights　reserved.