We study a limiting case of the nonlinear Calderon-Zygmund theory to the inhomogeneous p(x)-Laplace system. We prove local BMO estimates under the assumption that the variable exponent p(x) satisfies the so-called vanishing log-Holder continuity. This result extends the work by Diening, Kaplicky and Schwarzacher (2012), where the BMO estimates for the p-Laplacian were established. The talk is based on joint work with Anna Kh. Balci and Lars Diening.