  In the triplectic quantization of general gauge theories, we prove a
`triplectic' analogue of the Darboux theorem: we show that the doublet of
compatible antibrackets can be brought to a weakly-canonical form provided the
general triplectic axioms of [BMS] are imposed together with some additional
requirements that can be formulated in terms of marked functions of the
antibrackets. The weakly-canonical antibrackets involve an obstruction to
bringing them to the canonical form. We also classify the `triplectic' odd
vectors fields compatible with the weakly-canonical antibrackets and construct
the Poisson bracket associated with the antibrackets and the odd vector fields.
We formulate the Sp(2)-covariance requirement for the antibrackets and the
vector fields; whenever the obstruction to the canonical form of the
antibrackets vanishes, the Sp(2)-covariance condition implies the canonical
form of the triplectic vector fields.
