A process for preparing stereoregular olefin polymers which comprises contacting an olefin having 2 to 18 carbon atoms with a catalyst composition for use in the polymerization of olefins, which comprises (a) a catalyst component containing magnesium, titanium, and a halogen, (b) an organoaluminum compound, and (c) 0.001 to 5 moles, per mole of the organoaluminum compound (b), of a stereoregularity-improving agent selected from the group consisting of aromatic monocarboxylic acid esters, silicon compounds having an Si--O--C or Si--N--C bond, acetal compounds, germanium compounds having a Ge--O--C bond, and nitrogen-or oxygen-containing heterocyclic compounds having an alkyl substituent;
- said catalyst component further containing an ingredient which is at least one member selected from the group consisting of keto-esters represented by the following formula (I):
- ##STR5## wherein R.sup.1 and R.sup.2 independently represent a univalent hydrocarbon group having 1 to 20 carbon atoms which may have a chloride substituent, and Z represents a divalent aromatic or polycyclic hydrocarbon group having 6 to 20 carbon atoms which may have a chlorine substituent, the R.sup.1 and R.sup.2 being selected from the group consisting of aliphatic hydrocarbons, alicyclic hydrocarbons, aromatic hydrocarbons, and polycyclic hydrocarbons;
- and
- said organoaluminum compound being selected from the group consisting of the compounds represented by the following general formulae (II) through (V):
- AlR.sup.3 R.sup.4 R.sup.5 (II)
- R.sup.6 R.sup.7 Al--O--AlR.sup.8 R.sup.9 (III) ##STR6## wherein R.sup.3, R.sup.4 and R.sup.5 independently represent a hydrocarbon group having 1 to 12 carbon atoms, a halogen atom or a hydrogen atom, with the proviso that at least one of R.sup.3, R.sup.4 and R.sup.5 represents a hydrocarbon group, R.sup.6, R.sup.7, R.sup.8, and R.sup.9 independently represent a hydrocarbon group having 1 to 12 carbon atoms, R.sup.10 represents a hydrocarbon group having 1 to 12 carbon atoms, and l is an integer of at least 2.