Desorption of benzene (C6H6) from solid water surfaces [compact amorphous solid water (c-ASW) and crystalline ice (CI)] during irradiation of ultrathin solid films with low energy (250-300 eV) electrons has been investigated. The observed desorption behaviour is complex but typically two desorption components, with particularly large cross-sections, were present in the observed signal. A fast component, with a cross-section up to 10(-15) cm(2), is attributed to desorption of isolated C6H6 molecules that are hydrogen-bonded to small clusters of water (H2O) molecules on the solid water surface. A slower component, with a cross-section of ca. 10(-17) cm(2), is attributed mainly to desorption from larger C6H6 islands on the solid water surface. Possible desorption mechanisms are proposed and astrophysical implications are discussed.