  Logarithmic representations of the conformal Galilean algebra (CGA) and the
Exotic Conformal Galilean algebra ({\sc ecga}) are constructed. This can be
achieved by non-decomposable representations of the scaling dimensions or the
rapidity indices, specific to conformal galilean algebras. Logarithmic
representations of the non-exotic CGA lead to the expected constraints on
scaling dimensions and rapidities and also on the logarithmic contributions in
the co-variant two-point functions. On the other hand, the {\sc ecga} admits
several distinct situations which are distinguished by different sets of
constraints and distinct scaling forms of the two-point functions. Two distinct
realisations for the spatial rotations are identified as well. The first
example of a reducible, but non-decomposable representation, without
logarithmic terms in the two-point function is given.
