  We present first results on the production of nuclei and antinuclei such as
(anti)deuterons, (anti)tritons, (anti)3He and (anti)4He in pp collisions at
$\s$ = 7 TeV and Pb-Pb collisions at $\sNN$ = 2.76 TeV. These particles are
identified using their energy loss (dE/dx) information in the Time Projection
Chamber of the ALICE experiment. The Inner Tracking System gives a precise
determination of the event vertex, by which primary and secondary particles are
separated. The high statistics of over 360 million events for pp and 16 million
events for Pb-Pb collisions give a significant number of light nuclei and
antinuclei (Pb-Pb collisions: \sim30,000 anti-deuterons($\bar{d}$) and \sim4
anti-alpha($\bar{^4He}$)). The predictions of various particle ratios from the
THERMUS model is also discussed.
