A triangular norm (t-norm for short) \(T\colon [0,1]^2\to [0,1]\) is said to be \(\alpha\)-migrative, for some \(\alpha\) in \(]0,1[\), if \(T(\alpha x,y)=T(x,\alpha y)\) for all \(x,y\) in \([0,1]\). In this paper, the authors investigate the class of all continuous t-norms that are \(\alpha\)-migrative for some \(\alpha\) in \(]0,1[\), and, in particular, they charaterize these t-norms in terms of their additive generator.