Design of lumped-element immittance inverters which support dual-frequency operation and tuning of both operational frequencies is presented. Unique properties of the dual-composite right/left-handed transmission lines (D-CRLH TL) give an opportunity to design immittance inverters with two non-multiple operational frequencies and a stop band between them. Replacement of capacitors of D-CRLH TL unit cells with variable ones enables inverter tunability. Tunability analysis of such immittance inverters is given. It is shown that a tuning range of the operational frequencies is limited by a tolerable variation of the inverter parameter. The design concept is verified by results of electromagnetic simulation and measured frequency characteristics of fixed (non-tunable) as well as tunable dual-frequency immittance inverters and dual-band filters using the inverters.