Bootstrap procedures for testing equality of robust means in the one-, two-, and multi-sample problems for asymmetrically distributed data with unequal shapes are described. The emphasis is on parametric procedures, but some results are provided for nonparametric procedures as well. In the parametric framework, it is assumed that a model with two parameters, shape and scale, can be used to approximatively describe the populations. Examples are contaminated Lognormal, Weibull, Gamma, and Pareto distributions. Robust estimators of the parameters are supposed to be available; the robust mean is then defined as the asymptotic value of the robust estimate of the model mean. In the nonparametric framework, the robust mean is the asymptotic value of some estimate that does not depend on a parametric model, e.g., a trimmed mean. A studentized test statistic is explored with the help of examples on simulated and real data. In order to estimate the null model, criteria for robust constrained model fitting, the constraint being the null hypothesis, are introduced and discussed. In the nonparametric case, a robust version of exponential tilting is provided. Parametric, semiparametric, and nonparametric bootstrap schemes for the computation of finite sample distributions are considered. The examples illustrate procedures that can be useful in practice. [Author]