We study versions of strict Mittag-Leffler modules relativized to a class
\cK (of modules), that is, \emph{strict} versions (in the technical sense of
Raynaud and Gruson) of \cK-Mittag-Leffler modules, as investigated in the
preceding paper, {\em Mittag-Leffler modules and definable subcategories}, in
this very series (as well as the arXiv)