Search for bound states in , , and systems is performed by employing coupled homogeneous integral Faddeev equations written in terms of -matrix components. Instead of the traditional partial-wave expansion, a direct integration with respect to angular variables is used in these equations, and three-body coupling in the phase space of each of the – – , – – , and – – systems is taken precisely into account within this approach. Two-body matrices are the only ingredient of the proposed method. In the case of two-body interaction, they are found by solving the coupled Lippmann–Schwinger integral equations for the – – system in the ( , ) state, the system in the ( , ) state, the – system in the ( , ) state, and the – – system in the ( , ) state. An updated version of the ESC16 microscopic model is used to obtain two-body , YY , and YN interactions generating matrices. Two-body NN interaction is reconstructed on the basis of the charge-dependent Bonn model. Direct numerical calculations of the binding energy for the systems being considered clearly indicate that either of the and systems has one bound state with binding energies of 4.5 and 5.5 MeV, respectively, and that the system has two bound states with binding energies of 2.7 and 4.4 MeV.