We consider a class of mixed fractional stochastic differential equations
(SDEs) driven by both standard and fractional Brownian motion. Such equations involve two stochastic integrals of different type, namely a classical Itô and a pathwise integral. We study the well-posedness of irregular SDEs in which the drift coefficient exhibits discontinuities. Thereby we establish a generalized Itô rule valid for functions with absolutely continuous derivative and applicable to solutions of mixed fractional SDEs. Additionally, regularity properties of solutions are discussed. Parts of the talk are based on joint works with David Nualart, Tommi Sottinen and Lauri Viitasaari.