Let \(I\) be a real compact interval. A function \(g: I\to I\) is iterable if there exists a \(G: I\times]0,\infty[\to I\), continuous in both variables and satisfying \(G[G(x,s),t]=G(x,s+t)\), \(G(x,1)=g(x)\) (\(x\in I\); \(s,t\in ]0,\infty[\)). \textit{M. C. Zdun} [Continuous and differentiable iteration semigroups (1979)] gave necessary and sufficient conditions for a continuous function to be iterable. The present author offers five alternative necessary and sufficient conditions for a continuous function \(f: I\to I\) to be ``almost iterable'' that is, for the existence of an iterable \(g: I\to I\) such that \(\lim_{n\to\infty}[f^ n(x)-g^ n(x)]=0\) (\(x\in I\)), and the convergence is uniform on the components of the set obtained by excluding the fixed points of \(f\) from the interval connecting the smallest and the greatest fixed point. (Of course, \(x\) is a fixed point of \(f\) if \(f(x)=x\), furthermore, \(f^ 1(x):=f(x)f^{n+1}(x):=f[f^ n(x)]\), \(n=1,2,\dots\).).