A theoretical study of the density of states of shallow-acceptor impurities in cylindrically shaped GaAs low-dimensional systems is presented. The acceptor states are described within a variational scheme in the effective-mass approximation and using an infinite confinement potential model. The density of impurity states is calculated for a homogeneous distribution of acceptor impurities within the low-dimensional heterostructure. For dimensions of the system in which the length is much larger than the radius we obtain two well-defined peaks, associated with accepters either at the on-centre position or at the edge position in the low-dimensional system. Ln addition, we have observed the appearance in the density of impurity states of an additional peak (with low relative intensity and binding energy) associated with impurities located near to the intersection between the cylindrical surface and the top or bottom end faces of the structure. The general behaviour we observed in the density of impurity states describes reasonably well the spectral features present in experimental and theoretical data about acceptor-related photoluminescence spectra in GaAs microcrystals, cylindrical GaAs quantum-well wires and cylindrically shaped finite-length GaAs heterostructures.146496500