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 = 7 TeV and Pb-Pb collisions at = 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() and \sim4 anti-alpha()). The predictions of various particle ratios from the THERMUS model is also discussed.

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