The prodn. of polyolefins (PO) by (co)polymerising olefins in the presence of catalysts consisting of (A) solid catalyst components and (B) organic metal cpds. is claimed. (A) is obtd. by standing (1) Si oxides and/or Al oxides, (2) Mg cpds. of formula Mg(OR1 )x X1 2-m (R1 = 1-20 C hydrocarbon residue; X1 = halogen; m = 0-2), and (3) Ti cpds. of formula Ti(OR2 )n X2 4-n (R2 = as R1 ; X2 = as X1 ; n = 0 or above o and below 4) in contact with each other in the presence of (4) straight chain monohydric alcohol cpds. of formula. R3 OH (R3 = 4-12C straight chain hydrocarbon), and standing the reaction prods. obtd. in contact with (5) internal olefins of formula R4 HC=CHR5 (R4 , R5 = 1-24C alkyl, aryl or aralkyl which are located at the cis position). Also claimed is the prodn. of PO by (co)polymerising olefins in the presence of catalysts consisting of (A) obtd. by standing (1), (2), (3), (6) organic Al cpds. of formula Al(OR6 )p R7 q X3 3-(p+q ) (R6 , R7 = as R1 ; X3 = halogen or H; p = 0 or above 0 and below 3; q = above 0 and below 3 or 3, p+q = above 0 and below 3 or (3) in contact with each other in the presence of (4), and standing the reaction prods. obtd. in contact with (5) and (B). Also claimed is the prodn. of PO by (co)polymerising olefins in the presence of catalysts consisting of (A) obtd. by standing (1) components obtd. by standing (1) in contact with (6), (2) and (3) in contact with each other in the presence of (4), and standing the reaction prods. obtd. in contact with (5), and (B). Also claimed is the prodn. of PO by (co)polymerising olefins in the presence of catalysts consisting of (A) obtd. by standing (1), (2), (3) and (6) in contact with each other in the presence of (4), and standing the reaction prods. obtd. in contact with (5), and (B). Also claimed is the prodn. of PO by (co)polymerising olefins in the presence of catalysts consisting of (A) obtd. by standing (1") components obtd. by standing (1) in contact with organic metal cpds. of formula MeR8 X4 z-1 (Me = Li or Mg; R8 = as R1 ; X4= halogen; z = valence of Me) and then standing the components obtd. in contact with (6), (2) and (3) in contact with each other in the presence of (4), and standing the reaction prods. obtd. in contact with (5), and (B).    ADVANTAGE -   Olefin (co)polymers, partic. -olefin homopolymers or ethylene, -olefin copolymers are obtd. in high activity. The polyolefins have high bulk densities, relatively large average particle dia(s), narrow particle size distributions and fine free fluidity and contain small amt. of fine particles.