As the first endeavour, the influence of a pulsatile flow on the large-amplitude bifurcation behaviour of viscoelastic microtubes subject to longitudinal pretention is studied with special consideration to chaos. The viscoelastic microtube is surrounded by a nonlinear spring bed. A modified size-dependent nonlinear tube model is developed based on a combination of the couple stress theory and the Euler–Bernoulli theory. Hamilton’s principle, as an equation derivation technique, and Galerkin’s procedure, as a discretisation technique, are used. Finally, the discretised differential equations of the pulsatile fluid-conveying viscoelastic microscale tube are solved using a time-integration approach. It is investigated that how the bifurcation response for both motions along the axial and transverse axes is highly dependent of the mean value and the amplitude of the speed of the pulsatile flow.