In　this　paper,　two　models　of　toxic　phytoplankton　and　zooplankton　with　strong　or　weak　Allee　effect　are　investigated.　It　is　discussed　whether　the　equilibria　are　stable　and　Hopf　bifurcation　exists.　When　the　strong　Allee　effect　rate　is　high　and　the　toxin-producing　rate　is　less,　both　of　two　species　will　remain　extinct.　However,　when　the　toxin-producing　rate　increases,　the　system　will　possess　either　a　stable　limit　cycle　or　a　coexistence　equilibrium.　When　the　weak　Allee　effect　rate　is　high,　the　immediate　toxin-producing　might　result　in　the　occurrence　of　coexistent　equilibrium　or　a　subcritical　(supercritical)　Hopf　bifurcation.　A　degenerate　Hopf　bifurcation　is　also　demonstrated　by　numerical　simulation,　where　the　inner　limit　cycle　is　stable　and　the　outer　one　is　unstable.　For　both　strong　Allee　effect　and　weak　Allee　effect　cases,　the　obtained　results　show　that　immediate　production　of　toxin　can　aid　in　the　survival　of　both　species　and　large　toxin-producing　will　be　detrimental　to　the　growth　of　zooplankton.　The　findings　in　this　research　can　be　viewed　as　a　complement　to　those　with　the　Allee　effect.