  Superconformal algebras embedding space-time in any dimension and signature
are considered. Different real forms of the $R$-symmetries arise both for usual
space-time signature (one time) and for Euclidean or exotic signatures (more
than one times). Application of these superalgebras are found in the context of
supergravities with 32 supersymmetries, in any dimension $D \leq 11$. These
theories are related to $D = 11, M, M^*$ and $M^\prime$ theories or $D = 10$,
IIB, IIB$^*$ theories when compactified on Lorentzian tori. All dimensionally
reduced theories fall in three distinct phases specified by the number of (128
bosonic) positive and negative norm states: $(n^+,n^-) = (128,0), (64,64),
(72,56)$.
