A catalytic composition for dehydrogenating C.sub.2 -C.sub.5 paraffins containing gallium, alumina, silica and optionally one or more alkaline or alkaline-earth metals characterized in that the gallium, expressed as Ga.sub.2 O.sub.3, is contained in a quantity of between 0.1 and 33.6 wt %, the silica is contained in a quantity of between 0.08 and 3 wt %, and the alkaline metal, expressed as oxide, is contained in a quantity of between 0 and 5 wt %, the remainder to 100 wt % being alumina in .delta. or .theta. phase or in .delta.+.theta. or .delta.+.theta.+.alpha. phase mixture, said catalytic composition being activated by:
- oxidation with air and/or oxygen or a mixture containing oxygen at least in a 5 vol % concentration in an inert gas, for a time of between 1 and 180 minutes, at a temperature of between 500.degree. and 1000.degree. C.;
- purging with an inert gas for a time of between 1 and 10 minutes;
- reduction with hydrogen or a mixture containing hydrogen in at least a 10 vol % concentration in an inert or reducing gas, for a time of between 1 and 120 minutes, at a temperature of between 450.degree. and 800.degree. C.