Abstract: In 1970 the physicist V. Efimov pointed out that a system of three different particles, such that the two-particle interactions are short-range and resonant, have an infinite number of bound states. This phenomenon is known as Efimov Effect and it is a paradigmatic example of the so-called universality of low-energy physics. We consider a system composed by two identical fermions of unitary mass and a third particle of mass mm. We assume that the interactions are short-range and that the two-particle subsystems do not have bound states. Moreover, we suppose that the subsystems composed by one of the fermions and the third particle have a zero-energy resonance. Under these assumptions we prove the existence of a mass threshold m∗m∗ such that if m<m∗m<m∗ then the number N(z)N(z) of eigenvalues of the three-particle Hamiltonian smaller than z<0z<0 is infinite and N(z)∼C(m)|log|z||N(z)∼C(m)|log|z|| as z→0z→0. On the other hand for m>m∗m>m∗ we show that the number of negative eigenvalues stays finite.