We provide a full account on our study of the cobalt-catalyzed carbonylative polymerization of N-alkylazetidines involving three representative monomers. The individual N-alkylazetidine monomers display different characteristics in the polymerization, allowing the incorporation of amine and ester units into the amide-based polymers. We will first present the synthesis and characterization of poly (amide-co-amine) with a gradient amine distribution. Then, we will describe how to control the ester distribution in poly(amide-co-ester)s. Poly(amide-co-ester)s containing multiple segments, within which the ester units distribute in a gradient fashion, will be compared with multiblock poly(amide-co-ester)s. Finally, we report our discovery of a novel chain transfer pathway via N-benzyl abstraction.