The authors present L operators both for the special case of Neumann's system and the Kowalewski-Chaplygin-Goryachev top. These are quantum systems integrable by the quantum inverse scattering (R-matrix) method. L operators, being 2*2 matrices, satisfy an algebra generated by an R matrix of the XXX type. The close connection between the two models is demonstrated. They carry out a non-obvious separation of variables and also give a dynamical group scheme for the eigenstate problem of Neumann's system. This separation differs from those in Euler angles and allows them to find eigenenergies in an effective way.