Current oscillations are described which occur in CdS crystals in the region of N‐shaped negative differential conductivity of photocurrent–voltage characteristics at relative low field strength (5 × 102 to 2 × 103 V/cm). The main characteristics of the oscillations and the conditions for their appearance have been investigated in detail. It is shown that the current oscillations are connected with a steady periodical motion of electrical domains. The dependence of the electron capture coefficient on the field strength has been established and the model of recombination instability is used to discuss the experimental results.