Field-cycled proton-electron double-resonance imaging (FC-PEDRI) is a technique developed to image the distribution of free radicals in biological samples. This technique is based on the Overhauser Effect that causes an enhancement in the NMR signal by saturating the ESR resonance of unpaired electrons in the sample. FC-PEDRI requires two sources of RF irradiations. To improve the sensitivity and to reduce power deposition in samples, new dual-tuned single coil designs were needed since existing dual-tuned single-coil designs known in the literature cannot operate at two widely separated frequencies. The theory of double-tuned circuits was examined and new circuit models were developed to identify the design requirements. Four new dual-tuned RF coils were developed, namely a dual-tuned split solenoidal coil (2.5 and 78 MHz), a combined saddle-birdcage (CS-B) coil (2.5 and 110 MHz), a 3-endring (3-ER) birdcage (2.5 and 56 MHz) and a 4-endring (4-ER) birdcage (2.5 and 74 MHz). A prototype coil for each design was built for performance evaluation studies and the parameters evaluated were: the Q factors, the signal-to-noise ratio, the transmit sensitivity and the field uniformity. The performance of the NMR-mode of the 3-ER and 4-ER designs was poor because the inherently low-inductance of the birdcage meant that high-value capacitors with high dissipation factors had to be used in the fabrication. A new construction method named as the multilayer self capacitance (MLSC) technique was developed to improve the efficiency of the 4-ER design by creating efficient capacitors within the conductors of the coil itself. The unloaded Q factor of the optimised 4-ER birdcage using the MLSC technique was 267 compared to 100 when commercial capacitors were used.