The present invention relates to a process for the production of olefinic compounds that can be used for the production of detergents, additives, lubricants and/or plastic materials, or components which can be used in the field of oil explorations and productions, and a hydrocarbon fuel or a fraction thereof, which comprises subjecting a mixture of glycerides having at least one unsaturated hydrocarbon chain, to metathesis reaction and, after separating the olefinic mixture obtained, effecting a hydrodeoxygenation and subsequently hydroisomerization process, so as to obtain the hydrocarbon fuel or a fraction thereof.