A study is made of the possible holonomy group types of a spacetime for whi
ch the energy-momentum tensor corresponds to a null or non-null electromagn
etic field, a perfect fluid or a massive scaler field. The case of an Einst
ein space is also included. The techniques developed are, in addition, appl
ied to vacuum and conformally flat spacetimes and contrasted with already k
nown results in these two cases. Examples are given.