Abstract: A programmable logic device is provided with phase-locked loop (“PLL”) circuitry that includes two serially connected PLL circuits. An input clock signal is processed by a first of the PLL circuits to produce an intermediate clock signal having a frequency different from the input clock signal frequency. The intermediate clock signal is processed by the second PLL circuit to produce a final modified clock signal having a frequency different from both the input clock signal frequency and the intermediate clock signal frequency. By providing two serially connected PLL circuits, each PLL circuit can be required to operate with frequencies in a narrower range than might otherwise be required in a single PLL circuit required to produce a given input-to-final frequency change. Other circuitry on the programmable logic device (e.g., input/output registers and programmable logic circuitry for processing data signals) is responsive to the input and final modified clock signals.