  We present the results from a multi-epoch survey of two regions of M33 using
the 3.5m WIYN telescope. The inner field is located close to the centre of the
galaxy, with the outer region situated about 5.1 kpc away in the southern
spiral arm, allowing us to sample a large metallicity range. We have data for
167 fundamental mode Cepheids in the two regions. The reddening-free Wesenheit
magnitude Wvi period-luminosity relations were used to establish the distance
modulus of each region, with mu_{inner} = 24.37 +- 0.02 mag and mu_{outer} =
24.54 +- 0.03 mag. The apparent discrepancy between these two results can be
explained by the significant metallicity gradient of the galaxy. We determine a
value for the metallicity parameter of the Period--Luminosity relation gamma =
d(m-M)/d log(Z) = -0.29 +- 0.11 mag/dex, consistent with previous measurements.
This leads to a metallicity corrected distance modulus to M33 of 24.53 +- 0.11
mag.
