In our previous paper we have shown that high-viscosity drops in two dimensional linear creeping flows with a nonzero vorticity component may have two stable stationary states. One state corresponds to a nearly spherical, compact drop stabilized primarily by rotation, and the other to an elongated drop stabilized primarily by capillary forces. In this talk we explore consequences of the early result for the dynamics of highly viscous drops. Using boundary-integral simulations and small-deformation theory we show that a quasi-static linear flow with a slow change of the rotational component gives rise to a hysteretic response of the drop shape, with rapid changes between the compact and elongated solutions at critical values of the vorticity. In flows with periodic variation of the rotational component we find chaotic drop behavior in a certain range of flow parameters. In random flows we obtain a bimodal drop-length distribution. Some analogies with the dynamics of vesicles and macromolecules are pointed out.