  In this paper, we investigate the transversality of pairs of CSS codes and
their use in the second generation of quantum repeaters (QR)s. We show that
different stations of quantum link can experience different errors. Considering
this fact, we suggest to use different CSS codes in different stations. We also
suggest to use $[[n, k]]$ codes with $k > 1$ as they are more efficient then
codes with $k = 1$. We establish sufficient and necessary conditions for a pair
of CSS codes to be non-local CNOT-transversal. We show that in contrast to the
well known CNOT transversality which states that two CSS codes should be the
same, less restrictive constraints are needed. Next, we establish sufficient
and necessary conditions for a code pair to be CZ-transversal.
