The complex form of the characteristic equation for the stress singula
rities of the order r(lambda-1) (0 < Re [lambda] < 1) for the dissimil
ar anisotropic wedges is derived Special attention is then focused on
the problems that are composed by two orthotropic materials. For such
problems the characteristic equation is expressed in real forms from w
hich the dependence of the singularities on the material parameters an
d wedge angles is investigated. The case of a single free-fixed wedge
problem is particularly studied in derail. Numerical results for sever
al special wedge geometries are also presented.