Let \(qG\) denote the quasivariety generated by a group \(G\). \textit{A. Fedorov} [VINITI, No. 5489-B87, Moscow (1987)] classified all finite nilpotent groups of class 2 generating quasivarieties which contain only finitely many subquasivarieties, and showed that for any other finite nilpotent group \(H\) of class 2, \(qH\) contains uncountably many subquasivarieties. Let \({\mathcal N}_ 2\) denote the variety of nilpotent groups of class at most 2 and \(F_ 2 ({\mathcal N}_ 2)\) its free group of rank 2. In this paper it is proved that if \(\mathcal N\) is a quasivariety of torsionfree nilpotent groups, then either \({\mathcal N} = qF_ 2({\mathcal N}_ 2)\) or \(\mathcal N\) contains uncountably many subquasivarieties. (\(qF_ 2 ({\mathcal N}_ 2)\) itself contains only three subquasivarieties.) Remarks: Note that there is a misprint in the original paper, \(qG\) really should be the quasivariety (as I have defined it) and not the variety, as it says there.