  Based on the recent work \cite{PII} we put forward a new type of
transformation for Lorentzian manifolds characterized by mapping every causal
future-directed vector onto a causal future-directed vector. The set of all
such transformations, which we call causal symmetries, has the structure of a
submonoid which contains as its maximal subgroup the set of conformal
transformations. We find the necessary and sufficient conditions for a vector
field $\xiv$ to be the infinitesimal generator of a one-parameter submonoid of
pure causal symmetries. We speculate about possible applications to gravitation
theory by means of some relevant examples.
