I cannot enlarge your photos enough to get a clear photo but believe that it is Downy Mildew.  It is not uncommon on basil.  There is no cure but basil is an annual herb here and the season is almost over so just remove your plants and toss them in the garbage. Or you could clip off the affected stem sections and  pick the unaffected leaves and use them or dry them for future use.  Make sure your container is thoroughly cleaned before using it next year to avoid it having a head start.  

Basil downy mildew | UMN Extension