Abstract
Stability analysis of ?-methods for functional differential equations based on the test equation $$\begin{gathered} y'(t) = ay(t - \lambda ) + by(t),t > 0 \hfill \\ y(t) = \psi (t),t \in \left[ { - \lambda ,0} \right] \hfill \\ \end{gathered} $$ ?>0, is presented. It is known thaty(t)?0 ast?? if and only if |b|<?a and we investigate whether this property is inherited by the numerical solution approximatingy.
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