The purpose of this two-part investigation is to shed light on the physical effects responsible for the threshold behavior of FM receiving systems, especially those applying negative frequency feedback (FMFB systems), and to obtain quantitative relations for optimal design of such systems. First a new method is applied (in Part I) to the description of threshold effects in conventional FM receivers, giving access to the phenomena implied in a more lucid and mathematically simpler manner than obtained by previous theoretical investigations of other authors. By use of suitable approximations the output spectra and signal-to-noise ratios can be derived from the amplitude distribution of the noise envelope. The mthematical expressions obtained are relatively simple and well suited to numerical evaluation. Numerical calculations carried out by computer agree very well with the results available in the literature for some relatively restricted cases. The new method is then applied to the more involved problem of deriving the output noise spectra, at and below threshold, of an FMFB system, a problem that cannot be solved by conventional, mathematically rigid methods. The results obtained are shown (in Part II) to be in complete agreement with measurements carried out on different systems. Rules for optimal design of FMFB systems are given which permit the lowest threshold value to be determined without impairment to overall system performance.