Calculations are reported of the probability of observation of various degrees of phase front nonlinearity, for two and three signals incident from different directions upon a phase-measuring array. It is assumed that the signals fade independently and that their amplitude probability densities are described by a Rayleigh law. The measure of phase front nonlinearity employed is the rms deviation from the best straight-line fit to the measured phases along a linear array. The worst-case condition is that of equal average powers in the incident signals. When there are two such signals present, it is shown that the probability is 0.5 that a single observation of the rms phase deviation will yield a result of 25° or less. When there are three equal-power signals present, the corresponding probability is 0.2. Experimental measurements over a 911-km mid-latitude path and a 2100-km auroral-zone path confirm the general behavior predicted by the theory. The experimental program included concurrent measurements using FMCW, CW, and single-sideband signals from a controlled transmitter. The range resolution capability of the FMCW signals was utilized to provide direction-of-arrival statistics on a mode-separated basis. The standard deviation of the direction of arrival varied from 0.3° for E mode signals to 1.4° for F2 high-angle signals. The CW and single-sideband signals were processed by selecting only those phase fronts with rms phase deviations of 10° or less. For these, direction-of-arrival standard deviations were in the range 0.6°–0.9° with slightly smaller deviations being observed for the CW signals.