The Alt-Grassberger-Sandhas N -body theory is used to study interaction of η-mesons with d, 3 He, and 4 He. Separable expansion of the subamplitudes is adopted to convert the integral equations into the quasi-two-body form. The resulting formalism is applied to fit the existing data for low-energy η production on few-nucleon targets. On the basis of this fitting procedure the scattering lengths a ηd , a η 3 He , a η 4 He as well as the subthreshold behaviour of the elementary ηN scattering amplitude are obtained.