Abstract.Let a collection y of generically immersed curves be given in an oriented surface G . To each component circle, associate a Gauss word by traveling once around the circle and recording the crossing points with signs. The set of these words forms a Gauss paragraph. If y{ and y2 fill the surface G in the sense that the complementary regions are disks, then there is a homeomorphism of G taking one to the other if and only if y, and y2 have isomorphic Gauss paragraphs. This notion of isomorphism is defined here; it ignores the choices made in defining the Gauss words.
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