We have observed a disturbing suppression effect in three-pulse ESEEM and HYSCORE spectra of systems with more than one nucleus coupled to the electron spin. For such systems, the ESEEM signal contains internuclear combination peaks of varying intensity. At the same time, the peaks at the basic ESEEM frequencies are reduced in intensity, up to the point of complete cancellation. For both three-pulse ESEEM and HYSCORE, the amplitude of a peak of a given nucleus depends not only on its modulation depth parameter k and the tau-dependent blind-spot term b, but also on k and b of all other nuclei. Peaks of nuclei with shallow modulations can be strongly suppressed by nuclei with deep modulations. This cross-suppression effect explains the observation that HYSCORE (1)H peaks are often very weak or even undetectable in the presence of strong (14)N peaks. Due to this distortion of intensities, ESEEM spectra have to be analysed very carefully. We present a theoretical analysis of this effect based on the product rules, numerical computations, and illustrative experimental data on Cu(gly)(2). In experiments, the impact of this cross suppression can be alleviated by a proper choice of tau values, remote echo detection, and matched pulses.