This　paper　is　concerned　with　the　boundedness,　exponential　stability　and　almost　sure　asymptotic　stability　of　stochastic　functional　differential　equations　(SFDEs)　with　Markovian　switching.　The　key　technique　used　is　the　method　of　multiple　Lyapunov　functions.　We　use　two　auxiliary　functions　to　dominate　the　corresponding　different　Lyapunov　functions　in　different　modes　while　the　diffusion　operators　in　different　models　are　controlled　by　other　multiple　auxiliary　functions.　Our　conditions　on　the　diffusion　operators　are　weaker　than　those　in　the　related　existing　works.　(C)　2016　The　Franklin　Institute.　Published　by　Elsevier　Ltd.　All　rights　reserved.