THIS DOCTORAL THESIS CONSTITUTES A CONTRIBUTION TO THE STUDY OF THE OSCILLATION OF THE SOLUTIONS OF NONLINEAR ORDINARY TWO - DIMENSIONAL DIFFERENTIAL SYSTEMS WITH ALTERNATING COEFFICIENTS, TO THE STUDY OF THE ASYMPTOTIC BEHAVIOR, THE NONOSCILLATION AND THE STABILITY OF THE SOLUTIONS OF NEUTRAL DELAY DIFFERENTIAL EQUATIONS, TO THE STUDY OF THE OSCILLATION AND THE NONOSCILLATION OF DIFFERENTIAL EQUATIONS WITH RETARDED OR ADVANCED ARGUMENTS AS WELL AS OF INTEGRODIFFERENTIAL EQUATIONS, AND TO THE STUDY OF THE OSCILLATION OF THE SOLUTIONS OF SOME CLASSES OF DIFFERENCE EQUATIONS.