Delay elements and delay lines having glitchless operation are disclosed. By way of example, apparatus for delaying an input signal comprises a reference current generator for generating a constant current, wherein the constant current is insensitive to a variation of a power supply voltage, at least one variable bias voltage generator coupled to the reference current generator for generating a set of bias voltages based on the constant current generated by the reference current generator and a digitally programmable delay control input, and at least one delay element coupled to the at least one variable bias voltage generator for delaying the input signal by a constant delay which is determined by the set of bias voltages generated by the at least one variable bias voltage generator.