The apsidal motion analysis of the eccentric eclipsing binaries: V799 Cas, CO Cep, V1136 Cyg, V345 Lac, V364 Lac and V402 Lac have been presented. The method described by Lacy (1992) has been used for the apsidal motion analysis. The apsidal motion pericids have been found to be 1229 +/- 235, 64,600 +/- 20,000, 586 +/- 6, 14,240 +/- 2800, 3502 +/- 582 and 242 +/- 60 yr for V799 Cas, CO Cep, V1136 Cyg, V345 Lac, V364 Lac and V402 Lac, respectively. The corresponding internal structure constant, log (k) over bar (2), for V799 Cas, V364 Lac and V402 Lac have been derived and compared to the theoretical values. (C) 2012 Elsevier B.V. All rights reserved.