The _ΛΛ⁶He and _Λ⁹Be hypernuclei are treated as the S = 0, T = 0 (for the former) and S = 1/2, T = 0 (for the latter) bound states of the three-cluster systems ΛΛα and Λαα, respectively. The cluster-reduction method is used to solve the s-wave differential Faddeev equations for these systems. On the basis of the MT I-III model, the ΛΛ interaction potential is specified in the form V_ΛΛ = 2 3V_NN. Phenomenological potentials are used to describe Λα and αα interactions. The binding energies of the _ΛΛ⁶He and _Λ⁹Be hypernuclei and the parameters of low-energy Λ-hyperon and α-particle scattering on a _Λ⁵He hypernucleus are calculated. It is shown that the proposed ΛΛ interaction potential makes it possible to reproduce faithfully the binding energy of the _ΛΛ⁶He hypernucleus and that scattering in the Λ_Λ⁵He system is similar to neutron scattering on a deuteron.