Backlund transformations for two new integrable partial differential equations

We give two new completely integrable sixth-order partial differential equa tions, together with their Lax pairs and Darboux transformations. From thes e last we are able to derive the corresponding Backlund transformations. A simple reduction of these partial differential equations yields an integrab le fourth-order ordinary differential equation for which a linear problem w as previously unknown. We give also a linear problem for this ordinary diff erential equation.