Aims. About thirty new times of minimum light recorded with photoelectric or CCD photometers were obtained for four earlytype eccentric-orbit eclipsing binaries CW Cep (P = 2. Their O−C diagrams were analysed using all reliable timings found in the literature, and elements of apsidal motion were improved. Results. We confirm relatively short periods of apsidal motion of about 46, 27, 76, and 124 years for CW Cep, V478 Cyg, AG Per, and IQ Per, respectively. The corresponding internal structure constants, log k 2 , are then found to be -2.12, -2.25, -2.15, and -2.36, under the assumption that the component stars rotate pseudosynchronously. The relativistic effects are negligible, being up to 8% of the total apsidal motion rate in all systems. Using the light-time effect solution, we have predicted a faint third component orbiting with a period of about 39 years for CW Cep.