We investigate the production of equatorial jets which demonstrate strong local superrotation in an atmospheric general circulation model of Mars. These westerly jets are driven by diurnal thermal tides, and their strength is shown to be closely related to the amount of dust in the atmosphere. The superrotating jets are strongest near to equinox and under conditions of high atmospheric dust loading. If there is sufficient dust, in amounts corresponding to dust storm conditions, the westerly equatorial jets can occur at any time of year and reach speeds of over 40 m/s, peaking between 10 and 20 km altitude. For more moderate dust amounts, typical of background levels on Mars, the jets are still strong when the subsolar point is close to the equator and latitudinally symmetric tidal modes are forced. Strong easterly retrograde winds are also found high above the equator, and it is shown that the thermal tides play a major role in their formation. This process is especially relevant close to equinox when the cross-equatorial meridional circulation is weak.