There are obtained conditions under which maps from Rn to itself are globally injective. In particular there are proved some partial results related to the Weak Markus-Yamabe Conjecture which states that if a vector field X: Rn → Rn has the property that, for all p ∈ Rn, all the eigenvalues of DX(p) have negative real part, then X has at most one singularity.