  We analyse the structure of the $\kappa=0$ limit of a family of algebras
$A_\kappa$ describing noncommutative versions of space-time, with $\kappa$ a
parameter of noncommutativity. Assuming the Poincar\'e covariance of the
$\kappa=0$ limit, we show that, besides the algebra of functions on Minkowski
space, $A_0$ must contain a nontrivial extra factor $A^I_0$ which is Lorentz
covariant and which does not commute with the functions whenever it is not
commutative. We give a general description of the possibilities and analyse
some representative examples.
