The even-even Cd nuclei near neutron number N = 66 are indicative of t
he presence of two rather distinct families of excitations: anharmonic
quadrupole vibrations and more deformed intruder particle-hole excita
tions. We discuss these excitations as mainly coexisting families of s
tates forming the global structure of these nuclei. Then, we investiga
te how local large perturbations can cause strong mixing between the t
wo families. The coupling is studied in detail and a particular set of
selection rules governing the mixing leads to the introduction of a n
ew basis in order to discuss the interaction between vibrational and i
ntruder 9 excitations. Numerical applications are carried out for Cd-1
12,114.