There is a problem with the proofs of [1], Lemma 4.4 and the related Theorems 4.5, 4.8 and 4.12 regarding the computation of zero-divisor cup-length of real Grassmann manifolds ${G_k({{\mathbb {R}}}^{n})}$. The correct statements and improved estimates of the topological complexity of ${G_k({{\mathbb {R}}}^{n})}$ will appear in a separate paper by M. Radovanović [2].