“…Our main motivation in studying such a class of degenerate differential operators is to push the frontier for the solvability in presence of multiple characteristics. Besides the papers [1], [4], [9] and [8] (in which a case with non-smooth coefficients is studied), and the book [13] (where one can find an updated account of the solvability issue under the (Ψ) condition of Nirenberg and Treves, problem solved by Dencker in [5]), we wish to recall a number of works related to the local solvability of operators with multiple characteristics, such as [21], [16,17], [14], [23,25], [20], [15], [12], [18], and [6,7] (see also [19] and references therein). In particular, among them we wish to single out the recent paper [7] by Dencker in which he introduces the class of sub-principal type operators (whose characteristics are involutive) for which he gave necessary conditions for local solvability, and the paper [18] by Parenti and Parmeggiani (see also [19]) in which they obtain semiglobal solvability results (with a loss of many derivatives) for operators with transversal multiple symplectic characteristics.…”