Bounds for the determinants of Nekrasov and $S$-Nekrasov matrices

Two-sided bounds on $|\det A|$ for Nekrasov and $S$-Nekrasov matriсes $A$ are obtained. It is shown that for Nekrasov matrices the new bounds improve the known bounds of Bailey and Crabtree. As to the $S$-Nekrasov matrices, introduced only recently, so far no bounds on their determinants have been suggested, as far as the author is aware.