Description of multipole resonances

New developments in the microscopic description of the multipole resonances (E2 and EO) are presented. Selfconsistent Generator Coordinate Method (GCM) calculations of the breathing (EO) mode in connection with new experimental data suggest a nuclear incompressibility K=200 MeV. The E2 and EO resonances involve 2hw excitations. The coupling to the continuum and the admixture of 2p2h excitations are therefore more important than for the giant dipole (E1) resonance. Continuum- and 2p2h - (RPA)random phase approximation calculations for the E2 isoscalar resonance are discussed. Futhermore it is tested if it is possible to describe with the same Skyrme type forces ground and excited (especially giant resonance) states. It is found that the Skyrme forces have to be generalized to be able to describe also the low lying collective states. Furthermore it is shown that Brueckner-Hartree-Fock RPA calculations with realistic forces reproduce nicely the giant multipole resonances