In the paper under review the author proves that the existence of generic polynomials and generic extensions [in the sense of \textit{D. J. Saltman}, Adv. Math. 43, 250-283 (1982; Zbl 0484.12004)] are equivalent over an infinite field. Here one calls a monic polynomial \(P(s_1,\dots,s_m;X) \in K(s_1,\dots,s_m)[X]\), where \(s_1,\dots,s_m\) are indeterminates over the field \(K\), generic for a group \(G\) if (i) the splitting field of \(P(s_1,\dots,s_m;X)\) over \(K(s_1,\dots,s_m)\) is a \(G\)-extension, i.e. a Galois extension of \(K(s_1,\dots,s_m)\) with Galois group isomorphic to \(G\), and (ii) every \(G\)-extension of a field \(L\) containing \(K\) is the splitting field (over \(L\)) of a polynomial \(P(a_1,\dots,a_m;X)\) for some \(a_1,\dots,a_m \in L.\) Using \textit{F. R. DeMeyer}'s result [J. Algebra 84, 441-448 (1983; Zbl 0521.12014)] one gets that the existence of a generic polynomial \(P\) with finite group \(G\) is equivalent to the existence of a generic polynomial \(P'\) with the stronger property that every Galois extension \(N/L\) with \(\text{Gal}(N/L) \leq G\) appears as the splitting field of a specialization of \(P'.\) Note that meanwhile \textit{G. Kemper} obtained an even stronger result (to appear in Manuscr. Math.): If a polynomial \(P\) is generic for a finite group \(G\) over an infinite field \(K,\) then every Galois extension \(N/L\) with \(K \subseteq L\) and \(\text{Gal}(N/L) \leq G\) appears as the splitting field of a specialization of \(P.\)