  The measurement of the deuteron and anti-deuteron production in the rapidity
range $-1 < y < 0$ as a function of transverse momentum and event multiplicity
in p-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV is presented.
(Anti-)deuterons are identified via their specific energy loss
$\rm{d}E/\rm{d}x$ and via their time-of-flight. Their production in p-Pb
collisions is compared to pp and Pb-Pb collisions and is discussed within the
context of thermal and coalescence models. The ratio of integrated yields of
deuterons to protons (d/p) shows a significant increase as a function of the
charged-particle multiplicity of the event starting from values similar to
those observed in pp collisions at low multiplicities and approaching those
observed in Pb-Pb collisions at high multiplicities. The mean transverse
momenta are extracted from the deuteron spectra and the values are similar to
those obtained for p and $\Lambda$ particles. Thus, deuteron spectra do not
follow mass ordering. This behaviour is in contrast to the trend observed for
non-composite particles in p-Pb collisions. In addition, the production of the
rare $^{3}{\rm{He}}$ and $^{3}\bar{\rm He}$ nuclei has been studied. The
spectrum corresponding to all non-single diffractive p-Pb collisions is
obtained in the rapidity window $-1 < y < 0$ and the $p_{\rm{T}}$-integrated
yield d$N$/d$y$ is extracted. It is found that the yields of protons,
deuterons, and $^{3}{\rm{He}}$, normalised by the spin degeneracy factor,
follow an exponential decrease with mass number.
