  We generalize the derivative expansion (DE) approach to the interaction
between almost-flat smooth surfaces, to the case of surfaces which are
optimally described in cylindrical coordinates. As in the original form of the
DE, the obtained method does not depend on the nature of the interaction. We
apply our results to the study of the static, zero-temperature Casimir effect
between two cylindrical surfaces, obtaining approximate expressions which are
reliable under the assumption that the distance between those surfaces is
always much smaller than their local curvature radii. To obtain the zero-point
energy, we apply known results about the thermal Casimir effect for a planar
geometry. To that effect, we relate the time coordinate in the latter to the
angular variable in the cylindrical case, as well as the temperature to the
radius of the cylinders. We study the dependence of the applicability of the DE
on the kind of interaction, considering the particular cases where Dirichlet or
Neumann conditions are applied to a scalar field.
