In this paper necessary and sufficient conditions of asymptotic stability independent of delay of a certain class of both the retarded and neutral types of delay differential systems are obtained. The stability conditions reduce to positivity of a quartic equation. Conditions for the latter in explicit form are given by the authors in an earlier publication. In addition, sufficient conditions for stability for a general order delay differential system independent of delay are also obtained. Such conditions are ascertained from the fact that a sufficient condition for any algebraic equation to have no positive real roots, is that all its coefficients be positive.