A next-to-leading order QCD fit was performed on the e+ p deep-inelastic-scattering data collected by the ZEUS experiment over the years 1996-1997. The gluon and quark densities of the proton have been extracted. Experimental systematic errors were considered in this analysis taking into account their point-to-point correlations. This allows a correct evaluation of the uncertainties in the extracted parton densities. In addition, the strong coupling constant, as, was determined simultaneously.