Classical　gyroscopic　continua　include　axially　moving　materials　and　spinning　structures.　The　gyroscopic　effect　of　the　axially　moving　material　is　pronounced　via　the　gyroscopic　coupling　among　the　basis　functions　in　the　same　motional　direction.　On　the　other　hand,　the　gyroscopic　coupling　of　the　spinning　structure　acts　in　the　two　different　directions　of　motion.　In　this　paper,　we　study　the　dynamics　of　a　beam　with　both　axial　moving　motion　and　spinning　motion　as　a　prototype　of　bi-gyroscopic　continua.　The　influence　of　bi-gyroscopic　effects　on　the　natural　frequencies,　modes,　and　stability　is　investigated　by　an　analytical　method　applied　to　the　discretized　equations　of　the　axially　moving　and　spinning　beam.　Distinct　bifurcation　series　of　the　eigenvalues　and　corresponding　physical　interpretations　are　discussed　by　numerical　display　of　the　modal　motions.　The　complex　modes　describing　both　whirling　motions　and　traveling　waves　are　investigated　in　detail　for　such　bi-gyroscopic　system.　New　interesting　phenomena　have　been　analyzed　numerically　and　important　conclusions　have　been　drawn　for　such　bi-gyroscopic　system.