Abstract: Let L be an alternating link in S³ and let L project on S² except near crossings of L where L lies on a bubble. If the projective diagram on S² has n crossings, then there are n bubbles. Thus are construced 2-spheres surfaces S²₊ and S²_- by the properties of the link. Let F be an incompressible and pairwise incompressible surface in S³-L, there is a collection of simple closed curves when the surface F is in a standard position. The surfaces are described by discussing the properties of F∩S²_±. The genus of the surface equals zero if the graph of F∩S²_± is special simple.

Key words: alternating link, genus, incompressible surface