It is the purpose of this paper to study the problem of internal (subjective) time by a novel approach. Until now, this topic has mainly been discussed under the aspects of philosophy, psychology, and neurobiology. By way of contrast, we consider processes within an (abstract) information-processing system that fulfills certain minimum requirements. In this context, a special operator algebra is formulated, which has similarities to those occurring in quantum theory. A specific problem related to parallel (concurrent) processes leads to a concept of time windows (time slices) within the context of the operator algebra; this theoretical finding is compatible with known results. Finally, some hints for possible experiments are given, and it will be briefly discussed how this concept is related to traditional ones.