A catalytic solid for the stereospecific polymerisation of alpha-olefins, obtained by heat treatment, in the presence of a halogenated activating agent, of a liquid material prepared by contacting TiCl.sub.4, pretreated with an electron-donor compound, with a composition (C) of the formula
- AlR.sub.p (Y) .sub.q X .sub.3-(p+q) (I)
- in which
- R represents a hydrocarbon radical;
- Y represents a group chosen from --OR', --SR' and --NR'R", in which R' and R" each represent a hydrocarbon radical or a hydrocarbon atom;
- X represents a halogen;
- p is an arbitrary number such that 0<p<3;
- and
- q is an arbitrary number such that 0<p<3;
- the sum (p+q) being such that 0<(p+q).ltoreq.3
- to precipitate a catalytic solid comprising a titanium trichloride complex.