A class of complete potential-density basis sets in cylindrical (R,phi,z)
coordinates is presented. This class is suitable for stability studies of
galactic disks in three dimensions and includes basis sets tailored for disks
with vertical density profiles that are exponential (exp(-|z|/\zn)), Gaussian
(exp(-(z/\zn)^2) or locally isothermal (sech^2(z/\zn)). The basis sets are
non-discrete and non-biorthogonal; however, the extra numerical computations
required (compared with discrete biorthogonal sets) are explained and
constitute a small overhead. The method of construction (and proof of
completeness) is simple and can be used to construct basis sets for other
density distributions that are best described in circular or elliptic
cylindrical coordinates. When combined with a basis set designed for spheroidal
systems, the basis sets presented here can be used to study the stability of
realistic disks embedded in massive halos.