  In this paper we show the existence and uniqueness of a solution for a
stochastic differential equation driven by an additive noise which is the sum
of two fractional Brownian motions with different Hurst parameters. The proofs
are based on the techniques of fractional calculus and Girsanov theorem. In
particular, we show that the regularization effect of the fractional Brownian
motion with the smaller Hurst index dominates.
