  We report on the studies of Transverse-Momentum-Dependent distributions
(TMDs) at a future fixed-target experiment --AFTER@LHC-- using the $p^+$ or Pb
ion LHC beams, which would be the most energetic fixed-target experiment ever
performed. AFTER@LHC opens new domains of particle and nuclear physics by
complementing collider-mode experiments, in particular those of RHIC and the
EIC projects. Both with an extracted beam by a bent crystal or with an internal
gas target, the luminosity achieved by AFTER@LHC surpasses that of RHIC by up
to 3 orders of magnitude. With an unpolarised target, it allows for
measurements of TMDs such as the Boer-Mulders quark distributions and the
distribution of unpolarised and linearly polarised gluons in unpolarised
protons. Using polarised targets, one can access the quark and gluon Sivers
TMDs through single transverse-spin asymmetries in Drell-Yan and quarkonium
production. In terms of kinematics, the fixed-target mode combined with a
detector covering $\eta_{\rm lab} \in [1,5]$ allows one to measure these
asymmetries at large $x^\uparrow$ in the polarised nucleon.
