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Linguistic aspects of narration have been investigated in healthy populations, in a wide variety of languages and speech genres with very different results. There is some evidence indicating that linguistic elements, such as speech rate (i.e., the measure indicating the amount of speech produced in a certain time period), mean length of utterance (MLU) (i.e., the index reflecting sentence grammatical structure), frequency of nouns and verbs, might be affected by non-linguistic factors such as sex. On the other hand, despite the existence of neuroimaging evidence of structural differences between males and females, it is yet unknown how such differences could explain between-sex disparities in linguistic abilities in natural speech contexts. To date, no study has evaluated discourse production elements in relation to sex differences and their neural correlates in terms of brain structure, a topic that could provide unique insights on the relationship between language and the brain. The aim of the present study was to determine sex differences in narrative skills in healthy adults and to investigate white and gray matter structural correlates of linguistic skills in each group. Twenty-seven male and 30 female (N = 57) right-handed, neurologically intact, monolingual Greek speakers, matched for age and years of education, participated. Narrations of a personal medical event were elicited. Linguistic elements of speech rate (words per minute), MLUs, frequency of nouns and verbs were calculated for each speech sample, by two independent raters. Structural 3D T1 images were segmented and parcellated using FreeSurfer and whole-brain between-sex differences in cortical thickness, cortical volume and surface area, were obtained. Between-group differences in white matter diffusion tensor scalars were examined via Tract-Based Spatial-Statistics and whole-brain tractography and automated tract delineation using Automated Fiber Quantification. Speech rate and noun frequency were significantly lower for men, while verb frequency was significantly higher for women, but no differences were identified for MLU. Regarding cortical measures, males demonstrated increased volume, surface area and cortical thickness in several bilateral regions, while no voxel-wise or tractography-based between-group differences in white matter metrics were observed. Regarding the relationship between sex and speech variables, hierarchical regression analyses showed that the superior/middle frontal cluster in surface area may serve as a significant predictor of speech rate variance, but only in females. We discuss several possible interpretations of how sex-related speech abilities could be represented differently in men and women in gray matter structures within the broad language network.