This article introduces the design of surface coils for multinuclear applications. The relative sensitivities of several NMR-visible nuclei of biological interest are considered, and the motivations to operate an RF coil at multiple frequencies, both sequentially and simultaneously, are reviewed. The design of nested surface coils is then developed. Magnetic fields generated by planar loop and butterfly coils are first introduced. The benefits of quadrature design are briefly considered, and methods for combining coils to produce a quadrature field are investigated. These designs are then extended to dual-nuclei coils using multiple, geometrically decoupled loops. The insertion of trap circuits into the low-frequency coil, as an alternative to geometric decoupling, is then considered. Finally, the optimum placement of filters is discussed to prevent noise injection from the RF power amplifiers and to prevent the preamplifiers from saturating during J-decoupling.