Atomic hydrogen diffuses in semiconductor lattices and binds to impurities by forming complexes that can lead to a full neutralization of the impurity effects. In the present paper, the structural, vibrational, electronic and magnetic properties of complexes formed by H in the Mn x Ga 1−x As (x=0.03) dilute magnetic semiconductor have been investigated by using fi rst-principles DFT-LSD and LDA+U theoretical methods. The results account for recent experimental fi ndings showing a H passivation of the electronic and magnetic properties of Mn in GaAs. Moreover, they show that electron correlation has crucial effects on the properties of H-Mn complexes.