An apparatus for counting the sheets of a stream of partly overlapping sheets wherein the leaders of the next-following sheets normally rest on the trailing ends of the preceding sheets has a transporting unit which defines a path having two mutually inclined portions with the second portion sloping downwardly at an angle of 15 to 90 degrees relative to the first portion so that the leaders of successive sheets are lifted off the trailing ends of the respective preceding sheets. A photocell generates signals on detection of successive leaders while the leaders are on their way from the first into the second portion of the path, i.e., while the leaders are separated from the trailing ends of the preceding sheets, and such signals are transmitted to a counter which regulates the conversion of sheets into a series of stacks containing preselected numbers of superimposed sheets. The photocell is installed substantially midway between the longitudinal marginal portions of the stream. The sheets which travel past the photocell are subjected to the deforming action of an endless belt or chain which causes the upper sides of the sheets to assume a concave shape with the deepmost portion of each sheet extending in parallelism with the direction of transport of the stream.