The ternary Ti(Oiso-C 3 H 7) 4-Al 2 (C 2 H 5) 3 Cl 3 /Mg(C 4 H 9) 2 catalyst polymerizes ethylene and copolymerizes it with 1-hexene but does not polymerize propylene. The catalyst contains several types of active centers with different kinetic parameters; they produce polymer components with different average molecular weights. The centers have similar reactivities in ethylene/1-hexene copolymerization reactions and produce copolymers with a relatively uniform compositional distribution. The catalyst can be used for synthesis of ethylene/1-alkene copolymers of the linear low-density polyethylene type. The principal advantages of the catalyst are high activity, stable kinetic behavior, low cost of all components and the ease of use: the catalyst is prepared in situ from three commercially available compounds readily soluble in aliphatic and aromatic hydrocarbons.