Using optical/near-IR broadband photometry together with Halpha emission line data, we attempt to constrain the star formation histories, ages, total stellar masses and stellar mass-to-light ratios for a sample of extremely blue low surface brightness galaxies. We find that, under standard assumptions about the stellar initial mass function, the Halpha equivalent widths of these objects appear inconsistent with recently suggested scenarios including constant or increasing star formation rates over cosmological time scales. In a critical assessment of the prospects of obtaining ages from integrated broadband photometry, we conclude that even with near-IR data, the ages are poorly constrained and that current observations cannot rule out the possibility that these objects formed as recently as 1-2 Gyr ago. Methods which could potentially improve the age estimates are discussed. The stellar masses of these galaxies are inferred to lie below 10^10 solar masses. This, in combination with low ages, could constitute a problem for current hierarchical models of galaxy formation, which predict objects of this mass to form predominantly early in the history of the universe. The possibility to use the ages of the bluest low surface brightness galaxies as a test of such models is demonstrated.
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