The present invention discloses improved catalysts for polymerizing or copolymerizing olefins and a process for the production of polyolefins comprising a polymerization or copolymerization of olefins by the use of said catalysts. According to the invention there is provided a process for the production of polyolefins by polymerizing or copolymerizing olefins using as the catalyst a solid component containing a titanium compound and/or a vanadium compound and an organometallic compound, said solid component comprising a substance obtained by co-pulverizing (1) a metal halide selected from the group consisting of magnesium halides and manganese halides, (2) a compound represented by the general formula B(OR).sub.n X.sub.3-n X3 in which n is a number of the range 0