REDUCTION OF SINGULAR LAGRANGIANS OF HIGHER-ORDER M. de Le\'on, Maria H. Mello and P. R. Rodrigues Abstract. Given a singular non-autonomous Lagrangian of higher order we construct a reduced evolution space of the same order and a local regular Lagrangian on it which is gauge equivalent to the original one. The general geometrical framework used is the theory of almost stable tangent geometry of higher order introduced in \cite{LORS}. We show that higher order almost stable manifols can be endowed with a local Poincar\'e-Cartan form via the inverse problem of Lagrangian Dynamics. Keywords. Singular, non-autonomous higher order Lagrangians, connections, inverse problem, reduction, almost stable tangent geometry. MS classification: Primary 58F05, 53C15, Secondary 53C05, 70H35, 70H05. PACS: 0320, 0240.