The　third-order　nonlinear　optical　(NLO)　properties　of　the　nonzero-bandgap　graphene　materials,　including　graphene　oxide　nanosheets,　graphene　oxide　nanoribbons,　graphene　quantum　dots,　and　corresponding　hybrid　glasses,　were　investigated　using　ns　and　ps　Z-scan　techniques　at　532　nm.　The　observed　nonlinear　absorption　effects　were　affected　by　laser　duration.　Reverse　saturable　absorption　was　observed　in　the　ns　regime,　while　saturable　absorption　dominated　in　the　ps　regime.　The　NLO　performance　was　enhanced　in　the　hybrid　glasses.　These　findings　open　up　new　possibilities　for　the　practical　application　of　graphene　materials　in　the　NLO　field.　©　2014　the　Partner　Organisations.