The present thesis deals with the appearance of nonlinear effects in the frequency response of lightweight structures with sub-surface cracks or delaminations and the possibilities of using the appearance of said nonlinearities to monitor the condition of the structure by a Structural Health Monitoring (SHM) method. It is observed if and if yes, for which parameters the presence of damages causes nonlinear effects like period doublings, higher harmonics and frequency responses which are dependet of the initial values. The higher harmonics are only observed in the experimental part, not in the calculations. In the first part of this thesis, these questions are examined by use of semianalytical calculations. For the semianalytical observations, first a piecewise linear single degree of freedom oscillator as described by Holmes  is examined, and the occuring nonlinear effects are discussed. Then, an analytical model for a simply supported two dimensional beam on a nonlinear foundation is developed. The equations of the single modes of this analytical model have the same form as the equation of the piecewise linear single degree of freedom oscillator. The next step is, to observe the response of two parallel simply supported beams. For both, the beam on foundation and the parallel beams extensive parameter studies are made. The parameter studies include variation of the stiffness ratio and the offset between the two beams and between the beam and the foundation. Furthermore the excitation force and the damping factor are varied. In the next step an approach for a more realistic analytical model, a beam with rectangular cross-section and a lengthwise orientated, flat sub-surface crack, is described but further observations are relinquished. In the second part of this thesis, experimental observations with the objective to confirm the semianalytical calculations are made. In the experimental part, the frequency response of a free hanging beam with rectangular cross-section and a lengthwise orientated, flat sub-surface crack is measured for different crack free openings.