Summary: Hamilton functions of classical deformed oscillators (\(c\)-deformed oscillators) are derived from Hamiltonians of \(q\)-deformed oscillators of the Macfarlane and Dubna types. A new scale parameter, \(l_q\), with the dimension of length, is introduced to relate a dimensionless parameter characterizing the deformation with the natural length of the harmonic oscillator. Contraction from \(q\)-deformed oscillators to \(c\)-deformed oscillators is accomplished by keeping \(l_q\) finite while taking the limit \(\hbar \to 0\). The \(c\)-deformed Hamilton functions for both types of oscillators are found to be invariant under discrete translations: the step of the translation for the Dubna oscillator is half of that for the Macfarlane oscillator. The \(c\)-deformed oscillator of the Macfarlane type has propagating solutions in addition to localized ones. Reinvestigation of the \(q\)-deformed oscillator carried out in the light of these findings for the \(c\)-deformed systems proves that the \(q\)-deformed systems are invariant under the same translation symmetries as the \(c\)-deformed systems and have propagating waves of the Bloch type.