We present the currently most accurate evaluation of the W boson mass, M_W,
in the Minimal Supersymmetric Standard Model (MSSM). The full complex phase
dependence at the one-loop level, all available MSSM two-loop corrections as
well as the full Standard Model result have been included. We analyse the
impact of the different sectors of the MSSM at the one-loop level with a
particular emphasis on the effect of the complex phases. We discuss the
prediction for M_W based on all known higher-order contributions in
representative MSSM scenarios. Furthermore we obtain an estimate of the
remaining theoretical uncertainty from unknown higher-order corrections.Comment: 38 pages, 25 figures. Minor corrections, additional reference