Summary: For an integer \(k\), define poly-Euler numbers of the second kind \(\widehat{E}_n^{(k)}(n=0,1,\dots)\) by \[\frac{Li_k(1-e{-4t})}{4\sinh t}=\sum^\infty_{n=0}\widehat{E}_n^{(k)}\frac{t^n}{n!}.\] When \(k=1\), \(\widehat{E}_n=\widehat{E}_n^{(1)}\) are Euler numbers of the second kind or complimentary Euler numbers defined by \[\frac{t}{\sinh t}=\sum^\infty_{n=0}\widehat{E}_n\frac{t^n}{n!}.\] Euler numbers of the second kind were introduced as special cases of hypergeometric Euler numbers of the second kind in [T. Komatsu and H. Zhu, “Hypergeometric Euler numbers, AIMS Math 5, 1284–1303 (2020)], so that they would supplement hypergeometric Euler numbers. In this paper, we give several properties of Euler numbers of the second kind. In particular, we determine their denominators. We also show several properties of poly-Euler numbers of the second kind, including duality formulae and congruence relations.