Real forms of quantum orthogonal groups, q-Lorentz groups in any dimension

We review known real forms of the quantum orthogonal groups SOq(N). New *-c onjugations are then introduced and we contruct all real forms of quantum o rthogonal groups. We thus give an RTT formulation of the *-conjugations on SOq(N) that is complementary to the U-q(g) *-structure classification of Tw ietmeyer. In particular, we easily find and describe the real forms SOq(N-1 ,1) for any value of N. Quantum subspaces of the q-Minkowski space are anal yzed.