In this paper we consider the product of the harmonic Bergman projection Ph : L2(D) → L2h(D) and the operator of logarithmic potential type defined by L f (z) = − 12pi ∫ D ln |z − ξ| f (ξ)dA(ξ), where D is the unit disc in C. We describe the asymptotic behaviour of the eigenvalues of the operator (PhL)∗(PhL). More precisely, we prove that lim n→+∞n 2sn(PhL) = √ 4pi2 3 − 1