This study analyzes the nonlinear properties of the EEG at transition points of the sequences that build the Cyclic Alternating Pattern (CAP). CAP is a sleep phenomenon built up by consecutive sequences of activations and non-activations observed during the sleep time. The sleep condition can be evaluated from the patterns formed by these sequences. Eleven recordings from healthy and good sleepers were included in this study. We investigated the complexity properties of the signal at the onset and offset of the activations. The results show that EEG signals present significant differences (p<0.05) between activations and non-activations in the Sample Entropy and Tsallis Entropy indices. These indices could be useful in the development of automatic methods for detecting the onset and offset of the activations, leading to significant savings of the physician's time by simplifying the manual inspection task.