  We review known real forms of the quantum orthogonal groups SO_q(N). New
*-conjugations are then introduced and we contruct all real forms of quantum
orthogonal groups. We thus give an RTT formulation of the *-conjugations on
SO_q(N) that is complementary to the U_q(g) *-structure classification of
Twietmeyer \cite{Twietmeyer}. In particular we easily find and describe the
real forms SO_q(N-1,1) for any value of N. Quantum subspaces of the q-Minkowski
space are analized.
