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High-resolution absorption spectra of adenine, 9-methyladenine and 2-aminopurine in helium nanodroplets have been recorded. In contrast to molecular beam experiments, large variations in linewidths are observed for adenine and 9-methyladenine. At the same time, the spectrum of 2-aminopurine remains sharp upon solvation in helium droplets. The line broadening observed for adenine and 9-methyladenine is attributed to a significant decrease of the lifetime of the 1Lb(pp*) state and of 1np* levels vibronically coupled to this state. The origin of the lifetime reduction is argued to be related to the increased accessibility of the 1np*/1Lb(pp*) conical intersection upon solvation of these molecules in liquid helium.