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The transport properties of thin-film solar cells based on wide-gap CuGaSe(2) absorbers have been investigated as a function of the bulk [Ga]/[Cu] ratio ranging from 1.01 to 1.33. We find that (i) the recombination processes in devices prepared from absorbers with a composition close to stoichiometry ([Ga]/[Cu] = 1.01) are strongly tunnelling assisted resulting in low recombination activation energies (E(a)) of approx. 0.95 eV in the dark and 1.36 eV under illumination. (ii) With an increasing [Ga]/[Cu] ratio, the transport mechanism changes to be dominated by thermally activated Shockley-Read-Hall recombination with similar E(a) values of approx. 1.52-1.57 eV for bulk [Ga]/[Cu] ratios of 1.12-1.33. The dominant recombination processes take place at the interface between CdS buffer and CuGaSe(2) absorber independently from the absorber composition. The increase of E(a) with the [Ga]/[Cu] ratio correlates with the open circuit voltage and explains the better performance of corresponding solar cells.