The effect of variation the cooling rate in a wide range between 10-2 and 103 K s-1 on solidification the relaxed melt of random isotactic copolymers of propylene with low amount of 1-hexene or 1-octene has been studied. Emphasis has been placed on the structure formation at rapid cooling and an evaluation of the conditions required to permit crystallization, mesophase formation, or suppression of any ordering. The presence of low amount of either 1-hexene or 1-octene co-units in the propylene chain decreases drastically the critical cooling rate required for suppression of crystallization from about 150–200 K s-1 in the homopolymer to about only 10 K s-1 in the copolymers; increasing the cooling rate beyond these limits allowed mesophase formation or even generation of fully amorphous samples. The study of the kinetics of formation of specific structures is completed by a complementary analysis of the X-ray structure, morphology and superstructure of the ordered phase. The hindrance of non-isothermal crystallization and mesophase formation of random copolymers of propylene with 1-hexene or 1-octene is compared with that in propylene–1-butene copolymers; addition of only 2–3 mol% 1-hexene or 1-octene into the propylene chain leads to even larger hindrance of the ordering process than the addition of more than 10 mol% 1-butene.