  Stochastic quantization offers the opportunity to simulate field theories
with a complex action. In some theories unstable trajectories are prevalent
when a constant stepsize is employed. We construct algorithms for generating an
adaptive stepsize in complex Langevin simulations and find that unstable
trajectories are completely eliminated. To illustrate the generality of the
approach, we apply it to the three-dimensional XY model at nonzero chemical
potential and the heavy dense limit of QCD.
