In this chapter, delay differential equations with constant and timeperiodic coefficients are considered. The time delays are either constant or periodically varying. The stability of periodic solutions of these systems are analyzed by using the semidiscretization method. By employing this method, the periodic coefficients and the delay terms are approximated as constants over a time interval, and the delay differential system is reduced to a set of linear differential equations in this time interval. This process helps to define a Floquet transition matrix that is an approximation to the infinite-dimensional monodromy operator. Information on the stability of periodic solutions of the delay differential system is obtained from analysis of the eigenvalues of the finite linear operator. As illustrative examples, stability charts are constructed for systems with constant delays as well as timevarying delays. The results indicate that a semidiscretization-method-based stability analysis is effective for studying delay differential systems with time-periodic coefficients and periodically varying delays. The stability analysis also helps bring forth the benefits of variable spindle speed milling operations compared to constant spindle speed milling operations.