ESR and magnetization measurements have been performed up to 14 T in the compound CuGeO3. Two kinds of magnetic transitions are observed, between excited states and from the ground state. The former result essentially from a Zeeman splitting of the S = 1 magnetic triplet state characterizing the spin Peierls gap which exists at the wave vector Q = [1, 1, 1] of the magnetic Brillouin zone. The latter provide the first evidence of a Zeeman splitting on a spin Peierls gap. It is observed at Q = [0, 0, 0].