© 2015, The Author(s). A search for neutrinoless ββ decay processes accompanied with Majoron emission has been performed using data collected during Phase I of the GERmanium Detector Array (GERDA) experiment at the Laboratori Nazionali del Gran Sasso of INFN (Italy). Processes with spectral indices n = 1, 2, 3, 7 were searched for. No signals were found and lower limits of the order of 1023 yr on their half-lives were derived, yielding substantially improved results compared to previous experiments with 76Ge. A new result for the half-life of the neutrino-accompanied ββ decay of 76Ge with significantly reduced uncertainties is also given, resulting in (Formula presented.) yr.