Let K be an imaginary quadratic field and let F be an abelian extension of K. It is known that the order of the class group Cl_F of F is equal to the order of the quotient U_F/El_F of the group of global units U_F by the group of elliptic units El_F of F. We introduce a filtration on El_F made from the so-called truncated Euler systems and conjecture that the associated graded module is isomorphic, as a Galois module, to the class group.