Aims. Despite recent progress in the field, there are still many open questions regarding γ-ray binaries. In this paper we provide an overview of non-transient γ-ray binaries and discuss how observations with the Cherenkov Telescope Array (CTA) will contribute to their study. Methods. We simulated the spectral behaviour of the non-transient γ-ray binaries using archival observations as a reference. With this we tested the CTA capability to measure the spectral parameters of the sources and detect variability on various timescales. Results. We review the known properties of γ-ray binaries and the theoretical models that have been used to describe their spectral and timing characteristics. We show that the CTA is capable of studying these sources on timescales comparable to their characteristic variability timescales. For most of the binaries, the unprecedented sensitivity of the CTA will allow studying the spectral evolution on a timescale as short as 30 min. This will enable a direct comparison of the TeV and lower energy (radio to GeV) properties of these sources from simultaneous observations. We also review the source-specific questions that can be addressed with these high-accuracy CTA measurements.