We report the identification of extended Lyα nebulae at z ≃ 3.3 in the Hubble Ultra Deep Field (HUDF, ≃40 kpc × 80 kpc) and behind the Hubble Frontier Field galaxy cluster MACSJ0416 (≃40 kpc), spatially associated with groups of star-forming galaxies. VLT/MUSE integral field spectroscopy reveals a complex structure with a spatially varying double-peaked Lyα emission. Overall, the spectral profiles of the two Lyα nebulae are remarkably similar, both showing a prominent blue emission, more intense and slightly broader than the red peak. From the first nebula, located in the HUDF, no X-ray emission has been detected, disfavouring the possible presence of active galactic nuclei. Spectroscopic redshifts have been derived for 11 galaxies within 2 arcsec from the nebula and spanning the redshift range 1.037 < z < 5.97. The second nebula, behind MACSJ0416, shows three aligned star-forming galaxies plausibly associated with the emitting gas. In both systems, the associated galaxies reveal possible intense rest-frame-optical nebular emissions lines O iii λλ4959, 5007+Hβ with equivalent widths as high as 1500 Å rest frame and star formation rates ranging from a few to tens of solar masses per year. A possible scenario is that of a group of young, star-forming galaxies emitting ionizing radiation that induces Lyα fluorescence, therefore revealing the kinematics of the surrounding gas. Also Lyα powered by star formation and/or cooling radiation may resemble the double-peaked spectral properties and the morphology observed here. If the intense blue emission is associated with inflowing gas, then we may be witnessing an early phase of galaxy or a proto-cluster (or group) formation. © 2016 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society