I review my talk at Bedlewo, dealing with a differential system depending on deformation parametrs, with a Fuchsian singularity at z=0, and an irregular one at z=infinity of Poincare' rank 1. The eigenvalues of the leading matrix at
z=infinity may coalesce along a coalescence locus. In the recent paper with Cotti and Dubrovin, the isomonodromic deformation theory has been extended to this non-generic case, which was not considered by Jimbo, Miwa and Ueno. We explain this extension, with applications.
