  We consider $N$-body Schr\"odinger operators with a virtual level at the
threshold of the essential spectrum. We show that in the case of $N\geq 3$
particles in dimension $n\geq3$ virtual levels correspond to eigenvalues of the
system and we obtain decay rates of the corresponding eigenfunctions in
dependence on the dimension and the number of particles. We prove that in
dimension $n\geq 3$ the Hamiltonian of $N\geq 4$ particles interacting via
short-range potentials admits only a finite number of negative eigenvalues. We
extend our results to dimension $n=1$ and $n=2$ in case of $N\geq 4$ fermions.
