The　global　dynamics　of　Rayleigh–Duffing　oscillators　x¨　+　ax˙　+　bx˙　3+　cx+　dx3=　0　,　where　(a,b,c,d)∈{(a,b,c,d)∈R4:b≠0,d>0},　have　been　investigated　in　Chen　and　Zou　(J　Phys　A　49:165202,　2016).　In　this　paper,　the　complement　case　(a,b,c,d)∈{(a,b,c,d)∈R4:b≠0,d<0}　will　be　completely　studied,　where　the　bifurcation　diagram　includes　pitchfork　bifurcation,　Hopf　bifurcation,　and　heteroclinic　bifurcation.　Meanwhile,　the　global　phase　portraits　in　the　Poincaré　disc　are　given.　The　system　has　at　most　one　limit　cycle.　Moreover,　when　the　limit　cycle　exists,　its　corresponding　parameter　region　lies　between　Hopf　and　heteroclinic　loop　bifurcation　curves　in　the　parametric　space.　In　addition,　the　analytic　properties　of　the　heteroclinic　loop　bifurcation　curve　are　also　analyzed.　Finally,　a　few　numerical　examples　are　presented　to　verify　our　theoretical　results.　©　2018,　Springer　Science+Business　Media　B.V.,　part　of　Springer　Nature.