Males and females commonly compete for limited resources. When interaction costs are similar for both sexes and there are no sexual differences in resource value estimation, a non‐sex‐biased dominance is expected. Moreover, only non‐sex‐biased assessment of contenders fighting ability (Resource Holding Potential, RHP) should influence contest decisions. To test these predictions, we evaluated non‐breeding agonistic intra‐ and intersexual dyadic interactions in the weakly electric fish, Gymnotus omarorum. During the non‐breeding season, resource value is not expected to depend on individuals’ reproductive status and should thus be equal for males and females. In addition, as G. omarorum presents no sexual differences in body size, interaction costs can be considered symmetric between sexes. We confirmed that body size differences, but not individuals’ gender, is the best predictor of dominance. We correlated RHP asymmetries with contest duration and evidenced that body size but not sex influences assessment in intrasexual and intersexual encounters. All dyads tested engaged in agonistic interactions (N = 33) in which a clear dominant emerged. The analysis of conflict phases evidenced the submissive role of electric displays. Electric organ discharge (EOD) interruptions appear early in the contest as an electric hiding attempt, whereas chirps are post‐resolution signals of subordinate status. Interestingly, the decision of interrupting the EOD was also influenced by RHP asymmetries, whereas chirping activity was influenced by the intensity of the attacks received. Our results confirm that body size is the best RHP proxy in non‐breeding intra‐ and intersexual contests of this monomorphic species and demonstrated a sequential pattern of submissive signalling by means of two different electric displays.