The purpose of this contribution is to empirically implement and supplement the proposals made by Podinovski (2004b) to explore the nature of both global and local returns to scale in nonconvex nonparametric technologies. In particular, we both propose a simplified method to compute the global returns to scale and employ some secondary data sets to investigate the frequency of the special case of global sub-constant returns to scale. Furthermore, when determining global returns to scale using both convex and nonconvex technologies, we verify how often the resulting information is concordant or conflicting. Finally, besides comparing the FDH and DEA evolution of ray-average productivity for some typical individual observations, we introduce in the literature two original methods for the determination of local returns to scale in nonconvex technologies.