  The q-generalizations of the two fundamental statements of matrix algebra --
the Cayley-Hamilton theorem and the Newton relations -- to the cases of quantum
matrix algebras of an "RTT-" and of a "Reflection equation" types have been
obtained in [2]-[6]. We construct a family of matrix identities which we call
Cayley-Hamilton-Newton identities and which underlie the characteristic
identity as well as the Newton relations for the RTT- and Reflection equation
algebras, in the sence that both the characteristic identity and the Newton
relations are direct consequences of the Cayley-Hamilton-Newton identities.
