In　this　paper,　linear　and　nonlinear　complex　modes　are　used　to　analyze　the　free　vibration　of　pipes　conveying　fluid　involving　the　gyroscopic　properties　of　the　system.　The　natural　frequencies,　complex　mode　functions　and　time　domain　responses　of　the　admissible　mode　functions　based　on　discretized　model　are　obtained　using　the　invariant　manifold　method　and　compared　with　those　of　the　continuous　model.　A　good　agreement　has　been　achieved　if　the　admissible　mode　functions　for　the　static　beams　are　adopted.　The　energy　contributions　of　different　admissible　modes　to　the　modal　motions　are　also　studied　which　explores　the　gyroscopic　coupling　variation　among　the　admissible　modes　for　different　fluid　velocities.　Nonlinear　complex　modes　are　constructed　for　the　nonlinear　case　and　the　morphology　of　the　modal　motions　is　demonstrated　for　different　initial　energy　to　show　the　contribution　of　the　nonlinear　terms.　＇Traveling　waves＇　are　found　for　the　transverse　vibrations　of　the　pipes　conveying　fluid　due　to　the　gyroscopic　effects,　contrary　to　the　＂standing　waves＂　found　for　the　pipes　without　moving　fluid.