The present invention provides synthetic polyisoprenes having a high cis-1,4 linkage content and a process for their preparation. The synthetic polyisoprenes according to the invention have a cis-1,4 linkage content, measured by carbon-13 nuclear magnetic resonance and/or medium-wave infrared radiation analysis, of greater than 99.0%. The process for the preparation of these synthetic polyisoprenes involve polymerizing, at a temperature of 0 C. or lower, isoprene in the presence of a catalytic system based on: a) a conjugated diene monomer, b) an organic phosphoric acid salt of one or more rare earth, c) an alkylaluminium alkylating agent of the formula AlR3 or HAlR2, and d) a halogen donor consisting of an alkylaluminium halide, wherein the salt is suspended in at least one inert, saturated aliphatic or alicyclic hydrocarbon solvent and the alkylating agent:rare earth salt molar ratio ranges from 1 to 5.