  The theory of noncommutative geometry provides an interesting mathematical
background for developing new physical models. In particular, it allows one to
describe the classical Standard Model coupled to Euclidean gravity. However,
noncommutative geometry has mainly been developed using the Euclidean
signature, and the typical Lorentzian aspects of space-time, the causal
structure in particular, are not taken into account. We present an extension of
noncommutative geometry \`a la Connes suitable the for accommodation of
Lorentzian structures. In this context, we show that it is possible to recover
the notion of causality from purely algebraic data. We explore the causal
structure of a simple toy model based on an almost commutative geometry and we
show that the coupling between the space-time and an internal noncommutative
space establishes a new `speed of light constraint'.
