Asymptotic robustness of estimators of scale parameter with respect to scale invariant bias oscillation function is studied for two types of disturbances. In the case of £-contamination, the most robust sequence of equivariant estimators for model distribution with a positive support and the most robust sequence of equivariant symmetric estimators for symmetric model distribution are constructed. In the case of Kolmogorov-Levy neighbourhoods, the solution is derived without any assumptions about the model distribution. As examples, the most bias-robust estimators for uniform, Pareto, Weibull, Laplace, normal, Cauchy and double-exponential distributions are presented.
