Self-immolative polymers (SIPs) are a class of stimuli-responsive materials that undergo controlled end-to-end depolymerization in response to stimuli. Their unique degradation and amplification properties have made them of interest for a diverse array of applications including sensors, vehicles for controlled release, and transient objects. Thus far, a limited number of SIP backbones exists, each with its own advantages and limitations. We report here the preparation and study of polyglyoxylamides (PGAms) as a new class of SIPs. PGAms were synthesized by simple post-polymerization modifications of poly(ethyl glyoxylate) (PEtG). While retaining the important stimuli-responsive depolymerization properties of polyglyoxylates, PGAms exhibited much different thermal properties, and some were even water-soluble. Furthermore, a depolymerizable PGAm analogue of poly(ethylene glycol) was prepared, demonstrating the capability to synthesize more complex PGAm graft copolymers. Overall, PGAms are a new class of SIPs with unique combinations of physical, thermal, and degradative properties that provide avenues for novel applications.