Real classes of finite special unitary groups

We classify all real and strongly real classes of the finite special unitary group SUn(q). Unless q equivalent to 3. (mod4) and n vertical bar 4, the classification of real classes is similar to that of the finite special linear group SLn(q). We relate strong reality in SUn(q) to strong reality in the finite special orthogonal groups SOn +/- (q), and we classify real and strongly real classes in the last case for the group SOn +/- (q), when q is odd and n equivalent to 2 (mod 4).