<p>Robust inferential methods based on divergences measures have shown an appealing trade-off between efficiency and robustness in many different statistical problems. In this paper, minimum density power divergence estimators (MDPDEs) for the scale and shape parameters of the log-logistic distribution are considered. The log-logistic is a versatile distribution modeling lifetime data which is commonly adopted in Economics, Survival Analysis and Reliability Engineering, among others. In this paper it is shown that the classical estimators based on maximum likelihood (MLE) are included as a particular case of the MDPDE family. Moreover, we derive the asymptotic distribution of the MDPDEs. Besides, the corresponding influence function of the MDPDE is obtained, and its boundlessness is proved, thus showing that it leads to local robust estimators. This provides a difference with respect to MLE, which has an unbounded influence function. An extensive simulation study is carried out to illustrate the slight loss in efficiency of MDPDE with respect to MLE and, at besides, the considerable gain in robustness in the presence of contamination.</p>