We present both a theoretical and an experimental study of the long time behavior of membrane nanotubes pulled from giant unilamellar vesicles by molecular motors. Experimentally, two types of behaviors are observed, either tubes stall at a finite length or they undergo periodic oscillations. Theoretically we write the equations for the tube dynamics as a two-dimensional dynamical system where the variables are the tube length (or the force required to pull the tube at a given length) and the number of motors at the tip pulling the tube. We construct stability diagrams showing the stalling and oscillating states and present an example of oscillations in a non-linear regime. These results can explain the membrane tube retractions and oscillations observed in living cells.