  We extend the construction of open descendants to the $SU(2)$ WZW models with
non-diagonal left-right pairing, namely $E_7$ and the $D_{odd}$ series in the
$ADE$ classification of Cappelli, Itzykson and Zuber. The structure of the
resulting models is determined to a large extent by the ``crosscap
constraint'', while their Chan-Paton charge sectors may be embedded in a
general fashion into those of the corresponding diagonal models.
