Several extensions of the Standard Model and in particular superstring theories suggest the existence of axion-like particles (ALPs), which are very light spin-zero bosons with a two-photon coupling. As a consequence, photon-ALP oscillations occur in the presence of an external magnetic field, and ALPs can lead to observable effects on the measured photon spectrum of astrophysical sources. An intriguing situation arises when blazars are observed in the very-high-energy (VHE) bandnamely above 100 GeV -as it is the case with the presently operating Imaging Atmospheric Cherenkov Telescopes (IACTs) H.E.S.S., MAGIC, CANGAROO III and VERITAS. The extragalactic background light (EBL) produced by galaxies during cosmic evolution gives rise to a source dimming which becomes important in the VHE band and increases with energy, since hard photons from a blazar scatter off soft EBL photons thereby disappearing into e + e − pairs. This dimming can be considerably reduced by photon-ALP oscillations, and since they are energy-independent the resulting blazar spectra become harder than expected. We consider throughout a scenario first proposed by De Angelis, Roncadelli and Mansutti -to be referred to as DARMA for short -in which the above strategy is implemented with photon-ALP oscillations triggered by large-scale magnetic fields, and we systematically investigate its implications for VHE blazars. We find that for ALPs lighter than 5 · 10 − 10 eV the photon survival probability is larger than predicted by conventional physics above a few hundred GeV. Specifically, a boost factor of 10 can easily occur for sources at large distance and large energy, e.g. at 8 TeV for the blazar 1ES 0347-121 at redshift z = 0.188. This is a clear-cut prediction which can be tested with the planned Cherenkov Telescope Array and the HAWC water Cherenkov γ-ray observatory, and possibly with the currently operating IACTs as well as with detectors like ARGO-YBJ and MILAGRO. Moreover, we show that the DARMA scenario offers a new interpretation of the VHE blazars detected so far, according to which the large spread in the values of the observed spectral index is mainly due to the wide spread in the source distances rather than to large variations of their internal physical properties. Finally, we stress that ALPs with the right properties to produce the above effects can be discovered by the GammeV experiment at FERMILAB and more likely with arXiv:1106.1132v5 [astro-ph.HE] 22 May 2013 2 the planned photon regeneration experiment ALPS at DESY. PACS numbers: 14.80.Mz, 95.85.Pw, 95.85.Ry, 98.70.Rz, 98.70.Vc, 98.70.Sa