  Various double beta decay modes of Cd, Zn and Te isotopes are explored with
the help of CdTe and CdZnTe semiconductor detectors. The data set is splitted
in an energy range below 1 MeV having a statistics of 134.5 g$\cdot$d and one
above 1 MeV resulting in 532 g$\cdot$d. No signals were observed in all
channels under investigation. New improved limits for the neutrinoless double
beta decay of Zn70 of $T_{1/2} > 1.3 \cdot 10^{16} yrs$ (90% CL), the longest
standing limit of all double beta isotopes, and 0$\nu\beta^+$EC of Te120 of
$T_{1/2} > 2.2 \cdot 10^{16} yrs$ (90% CL) are given. For the first time a
limit on the half-life of the 2$\nu$ECEC of $^{120}$Te of $T_{1/2} > 9.4 \cdot
10^{15} yrs$ (90% CL) is obtained. In addition, limits on 2$\nu$ECEC for ground
state transitions of Cd106, Cd108 and Zn64 are improved. The obtained results
even under rough background conditions show the reliability of CdTe
semiconductor detectors for rare nuclear decay searches.
