We extend the notion of singular vectors to the context of Diophantine approximation of real numbers with elements of a totally real number field K. For $$m\ge 1$$ , we establish a version of Dani’s correspondence in number fields and prove that under a class of ‘friendly measures’ in $$K_S^m$$ , the set of singular vectors has measure zero. Here S is the set of Archimedean valuations of K and $$K_S$$ is the product of the completions of $$\sigma (K)$$ , $$\sigma \in S$$ . On the other hand, we show the existence of uncountably many non-trivial singular vectors on suitable submanifolds of $$K^m_S$$ under the action of a certain one parameter subgroup of $${\mathrm {SL}}_{m+1}(K_S)$$ .