This　paper　presents　a　dynamical　model　of　a　fluid-conveying　pipe　spinning　about　an　eccentric　axis.　The　coupled　bi-flexural-torsional　free　vibration　and　stability　are　analyzed　for　such　a　doubly　gyroscopic　system.　The　partial　differential　equations　of　motions　are　derived　by　the　extended　Hamilton　principle,　and　are　then　truncated　by　a　4-term　Galerkin　technique.　The　frequency　and　energy　evolutions　and　representative　mode　shapes　in　the　two　transverse　directions　and　torsional　direction　are　investigated　to　unveil　the　essential　dynamical　attributes　of　the　system.　It　is　indicated　that　the　stability　of　the　present　system　mainly　depends　on　spinning　speed,　flow　velocity　and　eccentricity,　while　the　torsional　frequencies　are　almost　immune　to　the　flow　velocity.　The　pipe　reveals　＇traveling-wave＇　modal　vibrations　in　both　transverse　directions,　and　a　general　＇standing-wave＇　modal　vibration　in　the　torsional　direction.