This slide show with written comments in pdf document format is essentially the slides and oral comments of a remote lecture given at the University of São Paulo on October 14, 2022. The thesis I defend is presented in its short summary: "Methodological variation is indispensable for many reasons. It has been managed until now by historical passages from one constituted methodology to another within different didactic configurations, or in the inter-methodological mode of eclecticism. Its management must now expand to the modes of multimethodology and plurimethodology." In a recent ("Modeling types of approach to methodological variation in language-culture teaching-learning: from eclecticism to complex didactics," https://www.christianpuren.com/mes-travaux/2021f-en/), I had proposed a modeling that focused on different conceptions of eclecticism. This conference focuses on the different ways in which methodological variation is carried out by teachers and authors of didactic materials using available methodological resources. The model crosses the four major modes of methodological variation - intra-, inter-, multi- and pluri-methodological - with the three levels of the methodological - micro, meso and macro - with eclecticism historically corresponding to inter-methodological variations at the micro and meso levels. The paper concludes with a table of "components of the teacher's complex management of methodological variation competence" that reuses, applying it to didactic cultures, the complex model of cultural competence (2011j), with its meta-, inter-, multi-, pluri-, co- and trans-cultural components. (Original French version: 2022g).