  We study non-rotating and isotropic strange quark stars in Lorentz-violating
theories of gravity, and in particular in Ho\v{r}ava gravity and
Einstein-{\ae}ther theory. For quark matter we adopt both linear and non-linear
equations of state, corresponding to the MIT bag model and colour flavour
locked state, respectively. The new structure equations describing hydrostatic
equilibrium generalize the usual Tolman-Oppenheimer-Volkoff (TOV) equations of
Einstein's general relativity. A dimensionless parameter $\nu$ measures the
deviation from the standard TOV equations, which are recovered in the limit
$\nu \rightarrow 0$. We compute the mass, the radius as well as the compactness
of the stars, and we show graphically the impact of the parameter $\nu$ on the
mass-to-radius profiles for different equations of state describing quark
matter. The energy conditions and stability criteria are also considered, and
they are all found to be fulfilled.
