Abstract: Log-Enriques surfaces are singular rational surfaces that arise as degenerations of Enriques surfaces. Even though they are rational, they carry Ricci-flat orbifold Kaeher metrics. Then one can construct an invariant of log-Enriques surfaces by using analytic torsion and volume. The goal of my talk is to explain that, as a function on the moduli space, this analytic torsion invariant is expressed as a nice automorphic form on the Kaehler moduli of a Del Pezzo surface.