Let \(X\) be a Hadamard space in the sense of Alexandrov, that is a simply connected complete geodesic metric space which is non-positively curved in the sense of Alexandrov [W. Ballmann, ‘Lectures on spaces of nonpositive curvature’ (DMV Seminar 25, Birkhäuser, Basel) (1995; Zbl 0834.53003); W. Ballmann, M. Gromov and V. Schroeder, ‘Manifolds of nonpositive curvature’ (Progress in Mathematics 61, Birkhäuser, Basel) (1985; Zbl 0591.53001)]. Suppose \(X\) contains a \(k\)-flat \(F\) of maximal dimension and consider quasiflats (i.e., quasi-isometric embeddings) \(f:\mathbb{R}^k\to X\) whose distance function from \(F\) satisfies a certain asymptotic growth condition. A known lemma of Mostow on quasiflats in symmetric spaces of non-compact type [G. D. Mostow, ‘Strong rigidity of locally symmetric spaces’ (Ann. Math. Studies 78, Princeton Univ. Pr.) (1973; Zbl 0265.53039)] is generalized here by the following result: the Hausdorff distance between \(f(\mathbb{R}^k)\) and \(F\) is uniformly bounded if \(X\) is locally compact and cocompact.