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We present strong approximations with rate of convergence for the solution of a stochastic dierential equation of the form dXt = b(Xt)dt + (Xt)dB H ; where b 2 C 1 b , 2 C 2 b , B H is fractional Brownian motion with Hurst index H, and we assume existence of a unique solution with Doss-Sussmann repre- sentation. The results are based on a strong approximation of B H by means of transport processes of Garzon et al (2009 (11)). If is bounded away from 0, an approximation is obtained by a general Lipschitz dependence result of Romisch and Wakolbinger (1985 (25)). Without that assumption on , that method does not work, and we proceed by means of Euler schemes on the Doss-Sussmann representation to obtain another approximation, whose proof is the bulk of the paper.

Approximations of fractional stochastic differential equations by means of transport processes