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Complementing the results of (Lotta and Nacinovich, Adv. Math. 191(1): 114-146, 2005), we show that the minimal orbit M of a real form G of a semisimple complex Lie group G(C) in a flag manifold M = G(C)/Q is CR-symmetric (see (Kaup and Zaitsev Adv. Math. 149(2):145-181, 2000)) if and only if the corresponding CR algebra (g, q) admits a Z(2) gradation compatible with the CR structure

CR-Admissible $$\mathbb{{Z}}_{2}$$ -gradations and CR-symmetries