Highly crosslinked polymers of varying structure were produced by the reaction of poly(glycidyl acrylate) (PGA) and methacrylate (PGM) with a variety of anhydride crosslinking agents: chlorendic (CA), glutaric (GA), maleic (MeA), succinic (SA), and polyrnalonic (pMnA) anhydrides. Topology was also varied by the use of a diluent and a comonomer in the backbone chain. Oxygen permeation measurements were made on these polymers coated onto a polypropylene film substrate before crosslinking. The crosslinking process greatly reduced the O2 permeability which, however, was dependent not only on the degree of crosslinking (yield of the crosslinking reaction), but also on the crosslink density, the chemical nature of the structural elements, and the topology of the polymer network. Thus the most impermeable coating (XPGA/CA) was made not from the stiffest and bulkiest components (PGM and CA), but by the reaction of the bulkiest anhydride (CA) with the more flexible polymer backbone chain (PGA). This is explained in terms of the need for chain flexibility to produce a crosslinked structure of optimum space filling character and network tightness.