In　this　paper,　an　analysis　is　made　for　the　unsteady　flow　due　to　an　expanding　cylinder　in　a　nanofluid　that　contains　both　nanoparticles　and　gyrotactic　microoganisms　with　suction.　The　nonlinear　system　of　partial　differential　equations　is　transformed　into　high-order　nonlinear　ordinary　differential　equations　using　similarity　transformations,　and　then　solved　numerically　using　a　shooting　method　with　fourth-fifth-order　Runge-Kutta　integration　technique.　The　influences　of　significant　physical　parameters　on　the　distributions　of　the　velocity,　temperature,　nanoparticle　volume　fraction,　as　well　as　the　density　of　motile　microorganisms　are　graphically　presented　and　discussed　in　detail.　It　is　found　that　dual　solutions　exist　for　both　stretching　and　shrinking　cases　and　the　range　of　dual　solutions　increases　with　the　strength　of　the　expansion.　The　results　also　indicate　that　larger　bioconvection　Peclet　number　and　smaller　Schmidt　number　lead　to　an　increased　concentration　of　microorganisms　and　thicker　boundary　layer　thickness.