We show that nonequilibrium spin fluctuations significantly influence the electronic transport in a single-electron transistor, when the spin relaxation on the island is slow compared to other relaxation processes, and when size effects play a role. To describe spin fluctuations we generalize the `orthodox' tunneling theory to take into account the electron spin, and show that the transition between consecutive charge states can occur via a high-spin state. This significantly modifies the shape of Coulomb steps and gives rise to additional resonances at low temperatures. Recently some of our predictions were confirmed by Fujisawa et al. [Phys. Rev. Lett. 88, 236802 (2002)], who demonstrated experimentally the importance of nonequilibrum spin fluctuations in transport through quantum dots.