A tale of two Nekrasov's integral equations

Just 100 years ago, Nekrasov published the widely cited paper \cite{N1}, in which he derived the first of his two integral equations describing steady periodic waves on the free surface of water. We examine how Nekrasov arrived at these equations and his approach to investigating their solutions. In this connection, Nekrasov's life after 1917 is briefly outlined, in particular, how he became a victim of Stalin's terror. Further results concerning Nekrasov's equations and related topicz are surveyed.