(I)n　this　paper,　the　nonlinear　dynamic　behaviors　of　two　elastic　rods　connected　by　a　joint　with　clearance　are　investigated.　The　rods　and　joint　system　are　modeled　by　two　degrees　of　freedom　of　mass-spring　system　with　a　clearance.　The　equations　of　motion　of　the　mass-spring　system　with　clearance　are　established　by　means　of　d＇Alembert＇s　principle.　Due　to　the　nonlinearity　caused　by　clearance,　the　dynamic　properties　of　the　system　are　studied　using　the　averaging　method　and　compared　with　numerical　solutions.　The　frequency　responses　of　the　system　subjected　to　cosinusoidal　excitation　are　obtained　as　well　as　the　effects　on　the　vibration　characteristics　induced　by　different　gap　sizes　are　investigated.　The　stability　condition　for　steady　solutions　is　presented　based　on　Lyapunov　theory.　The　method　for　detecting　the　multi-value　performances　of　the　frequency　response　has　been　proposed.　Based　on　this　method,　the　effects　of　the　clearance　size　on　the　multi-value　response　characteristics　are　investigated,　and　the　critical　value　of　the　clearance　is　obtained.　(C)　2014　Elsevier　Inc.　All　rights　reserved.