An \({\bar {\mathbb{R}}}^ d\)-valued random variable X is said to be sup selfdecomposable if for each \(t>0\) there is an \({\bar {\mathbb{R}}}^ d\)- valued random variable \(X_ t\) independent of X such that \[ (1)\quad X=^{d}(X-t\cdot 1)\vee X_ t, \] where \(=^{d}\) means equality in distribution and \(\vee\) means componentwise supremum. The equality (1) is motivated by the characterization \(X=^{d}e^{-t} X+X_ t\) of selfdecomposable measures. The author characterizes sup selfdecomposable measures as limit distributions, where partial sums are replaced by partial maxima. Also sup infinite divisible and sub stable measures are discussed.