  We study the simplest examples of minimal string theory whose worldsheet
description is the unitary (p,q) minimal model coupled to two-dimensional
gravity (Liouville field theory). In the Liouville sector, we show that
four-point correlation functions of `tachyons' exhibit logarithmic
singularities, and that the theory turns out to be logarithmic. The relation
with Zamolodchikov's logarithmic degenerate fields is also discussed. Our
result holds for generic values of (p,q).
