For　years　it　has　remained　a　problem　to　find　suitable　functionals　satisfying　certain　maximum　principles　associated　with　solutions　of　the　equation　(g(u)ui),　i　+　f(x,　u)　=　0.　In　this　paper,　maximum　principles　for　certain　functionals　which　are　defined　on　solutions　of　the　nonlinear　equations　subject　to　mixed　or　Robin　boundary　conditions　are　obtained.　The　principles　derived　may　be　used　to　deduce　bounds　on　important　quantities　in　physical　problems　of　interest.