AbstractMotivated by recent studies related to integrability of string motion in various backgrounds via analytical and numerical procedures, we discuss these procedures for a well known integrable string background (AdS5×S5)η. We start by revisiting conclusions from earlier studies on string motion in (ℝ ×S3)ηand (AdS3)ηand then move on to more complex problems of (ℝ ×S5)ηand (AdS5)η. Discussing both analytically and numerically, we deduce that while (AdS5)ηstrings do not encounter any irregular trajectories, string motion in the deformed five-sphere can indeed, quite surprisingly, run into chaotic trajectories. We discuss the implications of these results both on the procedures used and the background itself.