Part I of this text/reference presents techniques for linear systems with emphasis on asymptotic methods. The development in Part II employs the methods given in the first part and focuses attention on weakly nonlinear oscillatory systems and nonlinear difference equations. The stress is on practical methods, rather than on proof of theorems, and each method is illustrated by examples of applications in the sciences. Presents some numerical and graphical solutions generated by Lotus 1-2-3 and Math CAD.