Prediction of phenotypes from genetic data is considered to be the first practical application of data gained from association studies, with potential importance for medicine and the forensic sciences. Multiple genes and polymorphisms have been found to be associated with variation in human pigmentation. Their analysis enables prediction of blue and brown eye colour with a reasonably high accuracy. More accurate prediction, especially in the case of intermediate eye colours, may require better understanding of gene-gene interactions affecting this polygenic trait. Using multifactor dimensionality reduction and logistic regression methods, a study of gene-gene interactions was conducted based on variation in 11 known pigmentation genes examined in a cohort of 718 individuals of European descent. The study revealed significant interactions of a redundant character between the HERC2 and OCA2 genes affecting determination of hazel eye colour and between HERC2 and SLC24A4 affecting determination of blue eye colour. Our research indicates interactive effects of a synergistic character between HERC2 and OCA2, and also provides evidence for a novel strong synergistic interaction between HERC2 and TYRP1, both affecting determination of green eye colour.