Consider the delay differential equation $$\dot{x}\left(t\right)=g(x\left(t\right),x(t-r)),\left(1\right)$$ where $r>0$ is a constant and $g{ℝ}^2\to ℝ$ is Lipschitzian. It is shown that if $r$ is small, then the solutions of (1) have the same convergence properties as the solutions of the ordinary differential equation obtained from (1) by ignoring the delay.

In this paper we present an algebraic approach that describes the structure of analytic objects in a unified manner in the case when their transformations satisfy certain conditions of categorical character. We demonstrate this approach on examples of functional, differential, and functional differential equations.