Positron annihilation lifetime spectroscopy is used for investigation of low-density polyethylene and ethylene-methyl methacrylate copolymers of 1.45, 3.0, and 5.4 mole% of methyl methacrylate. The lifetime spectra are collected at 30 K, one by one, as a function of elapsed time. In the computer analysis a new theoretical model is developed, which enables separating the annihilation from positron free state, its trapped state and bound state in positronium. The positron trapping rate μ and the enhanced positronium formation rate κ are determined. The calculated values of μ and κ turned out to be linearly correlated. This correlation presumably originates from an influence of trapped electrons on the trapping of positrons. The dependences of κ on measurement time are determined for low-density polyethylene and ethylene-methyl methacrylate of different methyl methacrylate content. A theoretical model describing quantitatively the dependences is proposed. The model considers the processes of electron–ion recombination, electron trapping, and electron scavenging by dipolar carbonyl groups supplied by methyl methacrylate additives.