  Motivated by deformation quantization we investigate the algebraic GNS
construction of *-representations of deformed *-algebras over ordered rings and
compute their classical limit. The question if a GNS representation can be
deformed leads to the deformation of positive linear functionals. Various
physical examples from deformation quantization like the Bargmann-Fock and the
Schr{\"o}dinger representation as well as KMS functionals are discussed.
