We study the cross-migrativity of triangular norms. The classes of continuous triangular norms, which are cross-migrative with respect to some strict or nilpotent triangular norm, respectively, are completely characterized, as well as those which are cross-migrative with respect to the greatest and smallest triangular norms, respectively. As a by-product, parametric systems of equivalence relations on the classes of strict and nilpotent triangular norms are found. © 2012 Wiley Periodicals, Inc. © 2012 Wiley Periodicals, Inc.