  There are various analytical approaches to the mean electromotive force $\cal
E =< \vec{u}\times \vec{b}>$ crucial in mean--field electrodynamics, with
$\vec{u}$ and
  $\vec{b}$ being velocity and magnetic field fluctuations. In most cases the
traditional approach, restricted to the second--order correlation
approximation, has been used. Its validity is only guaranteed for a range of
conditions, which is narrow in view of many applications, e.g., in
astrophysics. With the intention to have a wider range of applicability other
approaches have been proposed which make use of the so--called
$\tau$--approximation, reducing correlations of third order in $\vec{u}$ and
$\vec{b}$ to such of second order. After explaining some basic features of the
traditional approach a critical analysis of the approaches of that kind is
given. It is shown that they lead in some cases to results which are in clear
conflict with those of the traditional approach. It is argued that this
indicates shortcomings of the $\tau$--approaches and poses serious restrictions
to their applicability. These shortcomings do not result from the basic
assumption of the $\tau$--approximation. Instead, they seem to originate in
some simplifications made in order to derive $\cal E$ without really solving
the equations governing $\vec{u}$ and $\vec{b}$. A starting point for a new
approach is described which avoids the conflict.
