The d + N systems are studied in a three-body model, using phenomenological N-N interactions. The scattering matrices are calculated by using the Kohn-Hulthén variational method. Then, they are analytically continued to complex energies and their singularities are localized. We find a virtual state at E = −1.66 MeV in 3 H and a pair of states at E = (−0.42 ± i0.52) MeV in 3 He relative to the d + N thresholds, respectively. In addition, we discuss some general aspects and problems of virtual states which may be useful also in the study of other systems, like 10 Li. PACS number(s): 21.45.+v, 24.30.Gd, 27.10.+h