The interplay of isotropic exchange, antisymmetric (AS) exchange, and electron delocalization has been theoretically investigated for a system comprising two triangles, one with three localized d¹ spins, which gives rise to spin frustration effects, and the other with one d¹ center delocalized on the three sites. In the localized limit the AS exchange is partially reduced by the low symmetry components of an isotropic exchange (inter-triangle interaction) and splits the spin triplets only in the second order, contrary to what is found for a single triangular system where splitting of the spin doublet levels occurs in the first order. Zero-field splitting parameters depend on both AS exchange parameters and low symmetry components of the isotropic exchange. The EPR spectrum consists of intratriplet (Heisenberg type) and intertriplet (non-Heisenberg type) lines. AS exchange also induces singlet-triplet transitions. The EPR spectra of powder samples are generated for a domain of key parameters. Two different situations occur depending on the symmetry of the electronic states when the electron delocalization is taken into account. The orbital doublets of the localized system indicate a complete averaging of the exchange interactions, which results in effective enhancement of AS exchange. Unlike triplets, the orbital singlets are unaffected by a transfer process, developing only second-order AS exchange. Coexistence of localized and delocalized states is expected to be an intrinsic feature of exchange systems with partial delocalization. The relevance of these effects to the magnetic properties of exchange clusters is briefly discussed.