The formation of excitons in OLEDs is spin dependent and can be controlled by electron-paramagnetic resonance, affecting device resistance and electroluminescence yield. We explore electrically detected magnetic resonance in the regime of very low magnetic fields (<1 mT). A pronounced feature emerges at zero field in addition to the conventional spin-1/2 Zeeman resonance for which the Larmor frequency matches that ofthe incident radiation. By comparing a conventional p-conjugated polymer as the active material to a perdeuterated analogue, we demonstrate the interplay between the zero-field feature and local hyperfine fields. The zero-field peak results from a quasistatic magnetic-field effect of the RF radiation for periods comparable to the carrier-pair lifetime. Zeeman resonances are resolved down to 3.2 MHz, approximately twice the Larmor frequency of an electron in Earth's field. However, since reducing hyperfine fields sharpens the Zeeman peak at the cost of an increased zero-field peak, we suggest that this result may constitute a fundamental low-field limit of magnetic resonance in carrier-pair-based systems. OLEDs offer an alternative solid-state platform to investigate the radical-pair mechanism of magnetic-field effects in photochemical reactions, allowing models of biological magnetoreception to be tested by measuring spin decoherence directly in the time domain by pulsed experiments.