For　a　stochastic　functional　differential　equation　(SFDE)　to　have　a　unique　global　solutionit　is　in　general　required　that　the　coefficients　of　the　SFDE　obey　the　local　Lipschitz　condition　and　the　linear　growth　condition.　However,　there　are　many　SFDEs　in　practice　which　do　not　obey　the　linear　growth　condition.The　main　aim　of　this　paper　is　to　establish　existence-and-uniqueness　theorems　for　SFDEs　where　the　linear　growth　conditionis　replaced　by　more　general　Khasminskii-type　conditions　in　terms　of　a　pair　of　Laypunov-type　function.