Heat-sealing polypropylene films having specific characteristics, and being well-balanced between a tensile modulus and a heat seal temperature, less tacky, and excellent in processability, transparency and impact resistance, as well as being excellent in resistance to whitening due to peeling, softness and impact resistance. A multilayered heat-sealing polyolefin resin laminate having at least one outermost layer produced from the above heat-sealing propylene polymers exhibits excellent low-temperature heat sealability and sufficient interlaminar strength without the use of an adhesive. The heat-sealing propylene polymers are produced by polymerizing propylene or polymerizing propylene with ethylene and/or C.sub.4-C.sub.20 .alpha.-olefin in the presence of a polymerization catalyst containing a transition metal compound represented by the following formula (I): ##STR00001## wherein A.sup.1, A.sup.2, E.sup.1, E.sup.2, M, X, Y, q and r are as defined in the specification.