Thermosetting polymers predominantly of a polybutadiene as a base polymer is disclosed, which polybutadiene is so configured as to have a vinyl content of not less than 40% by mol of the total monomer mol and a crosslink reactivity of at least 70% of the vinyl content. The cured polymer is ultrahighly resistant to heat and particularly applicable as an engineering plastics. Also disclosed is a process for producing the thermosetting polymer with the use of a specific initiator.