This paper proposes the design of tunable dual-band filters for multi-band multi-standard systems. The main objective is to provide frequency tunability in the second band while maintaining the first band fixed. To this end, the capacitive-loaded stepped-impedance resonator is used. The work is divided into two main parts. In the first part, a deep analysis of the capacitive-loaded stepped-impedance resonator structure is done, which provides analytical closed-form design equations which eases their design in front of the several approaches available in the literature up to now. The analysis is also particularized for the case of the capacitive-loaded uniform resonator. In the second part, resonators are integrated in two dual-band tunable filters.