  We report the identification of elongated (triaxial or prolate) galaxies in
cosmological simulations at $z\simeq2$. These are preferentially low-mass
galaxies ($M_s \le 10^{9.5} \ M_\odot$), residing in dark-matter (DM) haloes
with strongly elongated inner parts, a common feature of high-redshift DM
haloes in the $\Lambda$CDM cosmology. Feedback slows formation of stars at the
centres of these halos, so that a dominant and prolate DM distribution gives
rise to galaxies elongated along the DM major axis. As galaxies grow in stellar
mass, stars dominate the total mass within the galaxy half-mass radius, making
stars and DM rounder and more oblate. A large population of elongated galaxies
produces a very asymmetric distribution of projected axis ratios, as observed
in high-z galaxy surveys. This indicates that the majority of the galaxies at
high redshifts are not discs or spheroids but rather galaxies with elongated
morphologies.
