The paper deals with homogeneous random planar tessellations stable under iteration (random STIT tessellations). The length distribution of the typical I-segment is already known in the isotropic case~\cite{MNW07}. In the present paper, the anisotropic
case is treated. Then also the direction of the typical I-segment is of interest.

The joint distribution of direction and length of the typical I-segment is evaluated. As a first step, the corresponding joint distribution for the so-called typical remaining I-segment is derived.