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ABSTRACT We investigate the redshift evolution of the intrinsic alignments (IAs) of galaxies in the MassiveBlackII (MBII) simulation. We select galaxy samples above fixed subhalo mass cuts ($$M_h\gt 10^{11,12,13}\,\mathrm{M}_{\odot }\, h^{-1}$$) at z = 0.6 and trace their progenitors to z = 3 along their merger trees. Dark matter components of z = 0.6 galaxies are more spherical than their progenitors while stellar matter components tend to be less spherical than their progenitors. The distribution of the galaxy–subhalo misalignment angle peaks at ∼10 deg with a mild increase with time. The evolution of the ellipticity–direction (ED) correlation amplitude ω(r) of galaxies (which quantifies the tendency of galaxies to preferentially point towards surrounding matter overdensities) is governed by the evolution in the alignment of underlying dark matter (DM) subhaloes to the matter density of field, as well as the alignment between galaxies and their DM subhaloes. At scales $$\sim 1~\mathrm{Mpc}\, h^{-1}$$, the alignment between DM subhaloes and matter overdensity gets suppressed with time, whereas the alignment between galaxies and DM subhaloes is enhanced. These competing tendencies lead to a complex redshift evolution of ω(r) for galaxies at $$\sim 1~\mathrm{Mpc}\, h^{-1}$$. At scales $$\gt 1~\mathrm{Mpc}\, h^{-1}$$, alignment between DM subhaloes and matter overdensity does not evolve significantly; the evolution of the galaxy–subhalo misalignment therefore leads to an increase in ω(r) for galaxies by a factor of ∼4 from z = 3 to 0.6 at scales $$\gt 1~\mathrm{Mpc}\, h^{-1}$$. The balance between competing physical effects is scale dependent, leading to different conclusions at much smaller scales ($$\sim 0.1~\mathrm{Mpc}\, h^{-1}$$).