  We analyze the behaviour of heterotic squashed-Wess-Zumino-Witten backgrounds
under renormalization-group flow. The flows we consider are driven by
perturbation creating extra gauge fluxes. We show how the conformal point acts
as an attractor from both the target-space and world-sheet points of view. We
also address the question of instabilities created by the presence of closed
time-like curves in string backgrounds
