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The aim of this paper is to verify that the study of generic conformally flat hypersurfaces in 4-dimensional space forms is reduced to a surface theory in the standard 3-sphere.The conformal structure of generic conformally flat(local-)hypersurfaces is characterized as conformally flat(local-)3-metrics with the Guichard condition.Then,there is a certain class of orthogonal analytic(local-)Riemannian 2-metrics with constant Gauss curvature-1 such that any 2-metric of the class gives rise to a one-parameter family of conformally flat 3-metrics with the Guichard condition.In this paper,we firstly relate 2-metrics of the class to surfaces in the 3-sphere:for a 2-metric of the class,a 5-dimensional set of(non-isometric)analytic surfaces in the 3-sphere is determined such that any surface of the set gives rise to an evolution of surfaces in the 3-sphere issuing from the surface and the evolution is the Gauss map of a generic conformally flat hypersurface in the Euclidean 4-space.Secondly,we characterize analytic surfaces in the 3-sphere which give rise to generic conformally flat hypersurfaces.