  We deal with approximation of solutions of delay differential equations
(DDEs) via the classical Euler algorithm. We investigate the pointwise error of
the Euler scheme under nonstandard assumptions imposed on the right-hand side
function $f$. Namely, we assume that $f$ is globally of at most linear growth,
satisfies globally one-side Lipschitz condition but it is only locally H\"older
continuous. We provide a detailed error analysis of the Euler algorithm under
such nonstandard regularity conditions. Moreover, we report results of
numerical experiments.
