  We propose the full system of Baxter Q-functions (QQ-system) for the
integrable spin chains with the symmetry of the $D_r$ Lie algebra. We use this
QQ-system to derive new Weyl-type formulas expressing transfer matrices in all
symmetric and antisymmetric (fundamental) representations through $r+1$ basic
Q-functions. Our functional relations are consistent with the Q-operators
proposed recently by one of the authors and verified explicitly on the level of
operators at small finite length.
