Purpose: This study aimed to identify the genres that require second/foreign language learners to draw on their narrativecompetence along with the related level descriptors in the Common European Framework of Reference for Languages (CEFR)and the CEFR Companion Volume with New Descriptors, which serve to achieve coherence in the structuring of languagelearning/teaching processes by standardizing the way language ability is described.Design/Methodology/Approach: In this qualitative research, data were collected from the Common European Framework ofReference for Languages(2001) and the CEFR Companion Volume (2018) published by the Council of Europe through documentreview, and a content analysis was conducted. The processes of collecting, categorizing, and preparing the data for descriptionwere carried out sequentially.Findings: In the CEFR, written texts such as novels, personal letters, short stories, short newspaper articles (that describeevents), comic strips, photo stories, travelogues, news items, biographies, cartoons, advertisements, postcards, messages,notes, e-mails, blogs and fairy tales, which can be considered as narrative texts, are mentioned. In addition, personalnarratives, films, and anecdotes, which are not written genres, are also encountered. It has been found out that the leveldescriptors that can be functional in drawing inferences about whether the learners developed a narrative competence or notare structured gradually from level A to C in the CEFR. Upon analysis of the level descriptors regarding narrative texts andnarrative competence with respect to the four skills, it has been noted that the level descriptors that can be associated withnarrative texts and competence at all levels were the fewest in number regarding speaking and listening and the highestregarding reading.Highlights: Even though other genres are not referred to directly in the CEFR, a general framework about other genres is evidentin the text. The categorization of the narrativity-related level descriptors based on proficiency levels and skills is thought tocontribute to the designation of the learning objectives that reflect the language-specific features of narrative structures basedon the level descriptors in the CEFR, and thus to the enhancement of the quality of curriculum, materials, and activities to bedeveloped.