We present a theoretical analysis of quasicrystals ͑QCs͒ as potential thermoelectric materials. We consider a self-similar density of states model and extend the framework introduced in ͓G. D. Mahan and J. O. Sofo, Proc. Natl. Acad. Sci. U.S.A. 93, 7436 ͑1996͔͒ to systems exhibiting correlated features in their electronic structure. We show that relatively high values of the thermoelectric figure of merit, ranging from 0.01 up to 1.6 at room temperature, may be expected for these systems. We compare our results with available experimental data on transport properties of QCs and suggest some potential candidates for thermoelectric applications. © 2000 American Institute of Physics. ͓S0003-6951͑00͒03545-2͔During the last few years we have witnessed a growing interest in searching for high performance thermoelectric materials ͑TEMs͒. 1 The efficiency of thermoelectric devices depends on the transport coefficients of the constituent materials and it can be properly expressed in terms of the figure of merit ͑FOM͒ given by the dimensionless expression ϵZTϭ T S 2 /( e ϩ ph ) , where T is the temperature, is the electrical conductivity, S is the Seebeck coefficient and e and ph are the thermal conductivities due to the electrons and lattice phonons, respectively. The appealing question regarding what electronic structure provides the largest possible FOM was recently addressed by Mahan and Sofo 2 concluding that ͑i͒ the best TEM is likely to be found among materials exhibiting a sharp singularity ͑Dirac delta function͒ in the density of states ͑DOS͒ close to the Fermi level, and ͑ii͒, in that case, the effect of the DOS background contribution onto the FOM value may be quite dramatic: The FOM value being inversely proportional ͑in a marked nonlinear way͒ to the DOS value near the singularity.Quite interestingly the electronic structure of quasicrystalline alloys may satisfy these requirements in a natural way. In fact, thermodynamically stable quasicrystals ͑QCs͒ of high structural quality 3 exhibit unusual composition and temperature dependences of their transport coefficients, 4 which resemble more semiconductorlike than metallic character. 5 Theoretical efforts aimed to understand these anomalous transport phenomena have rendered two main results: ͑i͒ the existence of spiky features in the DOS near the Fermi level, 6 and ͑ii͒ the presence of a pronounced pseudogap at the Fermi level. 7