  We present the first extensive and detailed theoretical scenario for the
interpretation of Cepheid properties observed in the SDSS filters. Three sets
of nonlinear convective pulsation models, corresponding to the chemical
compositions of Cepheids in the Milky Way, the Large Magellanic Cloud and the
Small Magellanic Cloud respectively, are transformed into the SDSS bands by
relying on updated model atmospheres. The resulting observables, namely the
instability strip boundaries and the light curves, as well as the
Period-Luminosity, the Wesenheit and the Period-Luminosity-Colour relations,
are discussed as a function of the metal content, for both the fundamental and
the first overtone mode. The fundamental PL relations are found to deviate from
linear relations when computed over the whole observed Cepheid period range,
especially at the shorter wavelenghts, confirming previous findings in the
Johnson-Cousins bands. The obtained slopes are found to be mildly steeper than
the ones of the semiempirical and the empirical relations available in the
literature and covering roughly the same period range, with the discrepancy
ranging from about 13% in u-band to about 3% in z.
