  We study the cosmological evolution of the field equations in the context of
Einstein-Aether cosmology by including a scalar field in a spatially flat
Friedmann--Lema\^{\i}tre--Robertson--Walker spacetime. Our analysis is
separated into two separate where a pressureless fluid source is included or
absent. In particular, we determine the critical points of the field equations
and we study the stability of the specific solutions. The limit of general
relativity is fully recovered, while the dynamical system admits de Sitter
solutions which can describe the past inflationary era and the future late-time
attractor. Results for generic scalar field potentials are presented while some
numerical behaviours are given for specific potential forms.
