  In this paper, the polarization contents of Einstein-\ae ther theory and the
generalized TeVeS theory are studied. The Einstein-\ae ther theory has five
polarizations, while the generalized TeVeS theory has six. In particular,
transverse and longitudinal breathing polarization are mixed. The~possibility
of using pulsar timing arrays to detect the extra polarizations in
Einstein-\ae{}ther theory was also investigated. The analysis showed that
different polarizations cannot be easily distinguished by using pulsar timing
arrays in this theory. For generalized TeVeS theory, one of the propagating
modes travels much faster than the speed of light due to the speed bound set by
GW170817. In some parameter subspaces, the strong coupling does not take place,
so this theory is excluded.
