In many practical applications, a statistical description of waves is needed to calculate and predict their impact on ships, coastal structures and beaches. This paper investigates the statistics of the trough Th and the crest Cr of sea surface waves in the coastal zone of the Black Sea. The analysis uses data from direct wave measurements obtained on a stationary oceanographic platform of the Marine Hydrophysical Institute of the Russian Academy of Sciences. In all situations, the mode of the Th and Cr distributions is shifted to the region of higher values relative to the Rayleigh distribution mode. As a rule, the analysis of the distributions of trough and crest is carried out within a second-order nonlinear model based on the Stokes wave. It is shown that within the framework of this model it is possible to describe only the average distribution over an ensemble of situations, while for practical tasks it is necessary to know the deviations from these values. The type of Th and Cr distributions significantly depends on the skewness of the distribution of sea surface elevations Aη. With Aη < 0 the probability density function Th and Cr are almost identical. The second-order nonlinear model, in which the condition Aη > 0 is always fulfilled, does not describe this situation. The probability density functions Th and Cr obtained with Aη > 0 correspond qualitatively to this model. Changes in the excess kurtosis of the distribution of sea surface elevations have a lesser effect on the probability density functions Th and Cr.