The thermoelectric power, S, of metals is known to be linear with respect to temperature, T, in the low-temperature limit. The proportionality between the initial slope of the S(T) curve and the electronic specific-heat constant, gamma, both at the T = 0 limit, has been attracting attention for Cc compounds and other substances showing the heavy-Fermion state. However, there has been no study on solid solutions in relation to the present interest. We collected existing data of both S(T) and gamma on solid solutions based on Ce and Eu compounds, and we confirmed again the proportionality between the two quantities for their composition ranges covering the emergence of the heavy-Fermion state but having no magnetic order. The heavy-Fermion state in the Eu-based Compounds has never been investigated in relation to the present interest. The similarity between the valence-transition temperature, T-V, for Eu compounds and the Kondo temperature, T-K, for Ce compounds is discussed. Observations of the sign change in the S(T) curves and the existence of a peak in the p(T) curves, p being the resistivity, at around T-V for Eu compounds are noteworthy.