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The present paper is devoted to the classication of irregular sur- faces of general type with pg 3 and nonbirational bicanonical map. Our main result is that, if S is such a surface and if S is minimal with no pencil of curves of genus 2, then S is the symmetric product of a curve of genus 3, and therefore pg = q =3 and K 2 =6 . Furthermore we obtain some results towards the classication of minimal surfaces with pg = q = 3. Such surfaces have 6 K2 9, and we show that K2 =6i f and only if Sis the symmetric product of a curve of genus 3. We also classify the minimal surfaces with pg = q = 3 with a pencil of curves of genus 2, proving in particular that for those one has K2 =8 .

On the classification of irregular surfaces of general type with nonbirational bicanonical map