  We determine the possible gravitational wave polarizations in two general
classes of teleparallel gravity theories, using the metric and symmetric
teleparallel geometries. For this purpose we apply the Newman-Penrose
formalism, and find that depending on the choice of parameters, the
$\mathrm{E}(2)$ class of the theories is one of $\mathrm{N}_2, \mathrm{N}_3,
\mathrm{III}_5, \mathrm{II}_6$, corresponding to two to six polarizations,
where all of them include the two tensor polarizations known from general
relativity. We also find classes of theories apart from general relativity
which yield the same polarizations.
