Thermoplastic polymer compositions are disclosed which comprise the following components: (A) 1 to 99% by weight of an amorphous propylene polymer having the following characteristics: �.eta.!>1 dl/g, % of syndiotactic dyads (r)-% of isotactic dyads (m)>0, less than 2% of the CH.sub.2 groups contained in (CH.sub.2).sub.n sequences wherein n.gtoreq.2, Bernoullianity index=1.+-.0.2; and (B) 1 to 99% by weight of a propylene polymer having an essentially syndiotactic structure, optionally containing from 0.1 to 30% by moles of units deriving from .alpha.-olefins of formula CH.sub.2 .dbd.CHR in which R is an hydrogen atom or an alkyl group having from 2 to 10 carbon atoms. The compositions of the invention are endowed with good elasto-mechanical properties and are suitable for the production of low-temperature-heat-sealing films.