For the problem of estimating time difference of arrival (TDOA) of radio waves impinging on a pair of antennas for the purpose of passively locating the source of a communications or telemetry signal in the presence of interfering signals and noise, a new class of signal-selective algorithms that is highly tolerant to interference and noise is introduced. In part I of this two-part paper, the background theory of cyclostationary signals is presented and applied to the design of various new TDOA methods. In part II, algorithmic implementations are described and their performance capabilities are assessed by analysis and simulation. By virtue of the fact that the multiple-signal resolution problem is essentially eliminated in many applications by the signal selectivity of the algorithms, two performance advantages are gained: 1) the practicality of source location based on time-difference measurements with relatively closely spaced antennas is substantially enhanced, and 2) the problem of sorting through multiple TDOA estimates, resulting from multiple interferers, for the estimate corresponding to a particular signal of interest is eliminated. These new algorithms exhibit their signal selectivity regardless of the extent of temporal, spectral, or spatial overlap among received signals. It is only required that the signal of interest have a known (or measurable) analog carrier frequency or digital keying rate that is distinct from those of all interfering signals. Yet the computational complexity of these algorithms is comparable to that of conventional generalized cross-correlation algorithms.