Abstract: The invention relates to a polynorbornene-based rubbery composition with improved thermal behaviour, comprising a mixture of at least 50% by weight of polynorbornene and not more than 50% by weight of another rubber, the said mixture having been vulcanized by means of effective quantity of at least one compound: ##STR1## where R.sub.1, R.sub.2 =CH.sub.n X.sub.3-n, with X=F, Cl or Br and n = integer from 0 to 2; the invention also relates to a thermoplastic composition comprising 10-90 parts by weight (pw) of at least one olefin-based crystalline polymer (A), from 90-10 pw of a mixture (B) of at least 50% by weight of polynorbornene and not more than 50% by weight of another rubber, and a sufficient quantity of plasticiser for polynorbornene to lower its glass transition temperature to the range of rubbers, the sum of (A) and of (B) being equal to 100 pw and (B) being vulcanized by means of an effective quantity of at least one compound (I).