Conjecture: Let [Mscr ] and [Nscr ] be two matroids (possibly of infinite ranks) on the same set S. Then there exists a set I independent in both [Mscr ] and [Nscr ], which can be partitioned as I=H∪K, where sp[Mscr ](H)∪sp[Nscr ](K)=S. This conjecture is an extension of Edmonds' matroid intersection theorem to the infinite case. We prove the conjecture when one of the matroids (say [Mscr ]) is the sum of countably many matroids of finite rank (the other matroid being general). For the proof we have also to answer the following question: when does there exist a subset of S which is spanning for [Mscr ] and independent in [Nscr ]?