A process for dehydrogenating alkane or alkylaromatic compounds comprising contacting the given compound and a dehydrogenation catalyst in a fluidized bed. The dehydrogenation catalyst is prepared from an at least partially deactivated platinum/gallium catalyst on an alumina-based support that is reconstituted by impregnating it with a platinum salt solution, then calcining it at a temperature from 400° C. to 1000° C., under conditions such that it has a platinum content ranging from 1 to 500 ppm, based on weight of catalyst; a gallium content ranging from 0.2 to 2.0 wt %; and a platinum to gallium ratio ranging from 1:20,000 to 1:4. It also has a Pt retention that is equal to or greater than that of a fresh catalyst being used in a same or similar catalytic process.