The NEMO-2 tracking detector located in the Frejus Underground Laboratory was designed as a prototype of the detector NEMO-3 to study 0ν and 2ν double-beta decay (ββ) physics. After ten months of nearly continuous running with an enriched cadmium source (0.92 mol·y of116Cd) aββ2ν half-life ofT1/2=(3.75±0.35(stat)±0.21(syst))·1019 y was measured. Limits with 90% CL on the116Cd half-lives of 5.0·1021 y forββ0ν decay and of 1.2·1021 y forββ0νχ0 decay with a Majoron (χ0) were obtained. Theoretical predictions for 0ν and 2ν decays of116Cd are also presented.