We give a fully dynamic data structure for maintaining an approximation of the Hausdorff distance between two point sets in a constant dimension d, a standard problem in computational geometry. Our solution has an approximation factor of 1+epsilon for any constant epsilon >0 and expected update time O (logU/loglogn), where U is the universe size, and n is the number of the points. The result of the paper greatly improves over the previous exact method, which required O (n(5/6)polylogn) time and worked only in a semi-online setting. The model of computation is the word RAM model. (C) 2016 Elsevier B.V. All rights reserved.