In the present study, both linear and nonlinear EEG synchronization methods so called Coherence Function (CF) and Mutual Information (MI) are performed to obtain high quality signal features in discriminating the Central Sleep Apnea (CSA) and Obstructive Sleep Apnea (OSA) from controls. For this purpose, sleep EEG series recorded from patients and healthy volunteers are classified by using several Feed Forward Neural Network (FFNN) architectures with respect to synchronic activities between C3 and C4 recordings. Among the sleep stages, stage2 is considered in tests. The NN approaches are trained with several numbers of neurons and hidden layers. The results show that the degree of central EEG synchronization during night sleep is closely related to sleep disorders like CSA and OSA. The MI and CF give us cooperatively meaningful information to support clinical findings. Those three groups determined with an expert physician can be classified by addressing two hidden layers with very low absolute error where the average area of CF curves ranged form 0 to 10 Hz and the average MI values are assigned as two features. In a future work, these two features can be combined to create an integrated single feature for error free apnea classification.