The detection of underwater acoustic signals by simple auto‐ and cross‐correlation receivers in the presence of nonnormal, as well as normal background noise is examined on the basis of signal‐to‐noise ratios calculated from a generalized deflection criterion. Particular attention is devoted to the effects of impulse noise and mixtures of impulse and normal noise on system performance. Comparisons between system behavior vis‐à‐vis the two types of interference are made. For impulse noise equivalent in spectral distribution and average intensity to a Gaussian noise background it is found that the output signal‐to‐noise (power) ratios are related by the canonical expression(SN)I2 = (S/N)G21 + (1 − μ)Λ(S/N)G2, 0⩽μ⩽1, where Λ(⩾0) is the “impulse factor” and μ is the fraction (in average intensity) of the total noise background that is attributable to normal noise. Impulse noise always degrades system performance vis‐à‐vis normal noise in the autocorrelation reception of stochastic signals, characteristic of applications where passive receiving methods must be used. This degradation can be considerable [O(10 dB or more)] if the noise is highly impulsive (large Λ) and if large values of(S/N)out2(>0 dB)are required (for high accuracy of decision). On the other hand, when coherent (i.e., deterministic) signals are employed, so that cross‐correlation reception is possible, the degradation may be reduced essentially to zero (i.e., Λ → 0) under realizable conditions of operation. It is observed for impulsive, as well as normal noise backgrounds, that cross‐correlation receivers are linear in their dependence on signal‐to‐noise ratio, i.e.,(S/N)out2∼(S/N)in2if sufficiently strong injected signals are employed. The analysis is carried out largely in canonical form, so that the general results for(S/N)out2can be applied to other, special types of nonnormal noise backgrounds. Specific relations are included, along with a detailed summary of the principal results, showing the dependence of(S/N)out2on(S/N)in2, filtering, delay, noise and signal spectra, etc., for weak and strong inputs, little or heavy postcorrelation smoothing and for Gaussian as well as for impulse noise.