Samples of random copolymers consisting of 1-butene modified with a low ethylene content (4, 5, 8% by weight) produced with metallocene catalysts were studied to elucidate the polymorphic behavior of this new class of materials and to characterize them from a structural, morphological, and mechanical point of view. The samples cooled down from the melt are in amorphous phase and crystallize in a mixture of form I and I′ or in pure form I′ with aging time, according to the C2 content. Infrared and nuclear magnetic resonance spectroscopy, X-ray diffraction and microscopic techniques were used to follow the changes of the material with aging time and to correlate the structural and morphological behavior with the peculiar mechanical properties that differentiate the samples with increasing C2 content. The presence, in the aged samples with higher C2 content, of the pure form I′ induces the peculiar ability to self-welding and these copolymers combine high flexibility with good elasticity and ductility and can be processed directly or used as modifying agents in polymers. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40119.