Three-and four-neutron systems are studied within the framework of the hyperspherical approach with a local S-wave nn-potential. Possible bound and resonant states of these systems are sought as zeros of three-and fourbody Jost functions in the complex momentum plane. It is found that zeros closest to the origin correspond to sub-threshold (nnn) 1 2 − and (nnnn) 0 + resonant states. The positions of these zeros turned out to be sensitive to the choice of the nn-potential. For the Malfliet-Tjon potential they are E 0 ( 3 n) = −4.9 − i6.9 (MeV) and E 0 ( 4 n) = −2.6 − i9.0 (MeV). Movement of the zeros with an artificial increase of the potential strength also shows an extreme sensitivity to the choice of potential. Thus, to generate 3 n and 4 n bound states, the Yukawa potential needs to be multiplied by 2.67 and 2.32 respectively, while for the Malfliet-Tjon potential the required multiplicative factors are 4.04 and 3.59.