In　this　paper,　a　dynamical　model　of　simply-supported　spinning　pipes　conveying　fluid　with　axial　deployment　is　proposed　and　the　transverse　free　vibration　and　stability　for　such　a　doubly　gyroscopic　system　involving　time-dependent　parameters　are　investigated.　The　partial　differential　equations　of　motion　are　derived　by　the　extended　Hamilton　principle　and　then　truncated　by　the　Galerkin　technique.　The　time-variant　frequencies,　mode　shapes　and　responses　to　initial　conditions　are　comprehensively　investigated　to　reveal　the　dynamical　essence　of　the　system.　It　is　indicated　that　the　qualitative　stability　evolution　of　the　system　mainly　depends　on　the　effect　of　fluid-structure　interaction　(FSI),　while　the　spinning　motion　will　enhance　the　pipe　rigidity　and　eliminate　the　buckling　instability.　The　dynamical　evolution　of　a　retracting　pipe　is　almost　inverse　to　that　of　the　deploying　one.　The　pipe　possesses　different　mode　configurations　of　spatial　curves　as　the　pipe　length　increases　and　some　modal　and　response　characteristics　of　the　present　system　are　found　rather　distinct　from　those　of　deploying　cantilevered　structures.　(c)　2017　Elsevier　Ltd.　All　rights　reserved.