Using extensive first principles protocols, a systematic investigation is performed to probe the oxygen reduction reaction (ORR) mechanism on nitrogen (N) doped graphynes (Gys, e. g. αGy, βGy, γGy and 6,6,12Gy) and graphdiyne (Gdy) in alkaline medium. We considered both associative and dissociative pathways, as well as two distinct intermediate forks for each of them depending on the first protonation site(s). Following the dissociative approach, the activation energy to form an O 2 dissociated configuration is found as a function of the distances migrated by the O atoms over the catalyst surface and the amount of charge transferred from the C atoms linked to N. N doped αGy and 6,6,12Gy emerged as the best electrocatalyst comparing both pathways having lowest overpotentials of 0.88 and 0.82 V, respectively. The rate-limiting steps for the two different intermediate routes are observed to be dependent on the first protonation site(s) and related to the desorption of the OH radical from the sp hybridized C atom site(s) linked to N. Hence, the OH adsorption energy is identified as a descriptor for the efficiency of the ORR for the considered systems. The stabilities of the ORR intermediates are further elaborated in terms of pH and electrode potential.