Abstract. We consider the structure of the Kac modulesV(Λ) for dominant integral doubly atypical weights Λ of the Lie superalgebra s1(2/2). Primitive vectors ofV(Λ) are constructed and it is shown that the number of composition factors ofV(Λ) for such Λ is in exact agreement with the conjectures of [HKV]. These results are used to show that the extended Kac‐Weyl character formula which was proved in [VHKTl]for singly atypical simple modules of s1(m/n), and conjectured to be valid for all finite dimensional irreducible representations of sl(m/n) in [VHKT2] is in fact valid for all finite‐dimensional doubly atypical simple modules of s1(2/2).