Oscillations occur at many different levels of biologic processes, in genetic systems, signaling and as metabolic oscillations. Examples are circadian oscillations, the canonical NFκB-pathway, and calcium signaling. The oscillations differ not only in their functions and time-scale, i.e. period length, but also in the intensity of their response towards environmental changes, the so-called robustness or sensitivity of the particular response. Thereby, the period of calcium oscillations whose function is discussed to lie in frequency encoded signal transduction is known to be very sensitive. Contrariwise, the period of circadian rhythms is very robust; it has to remain nearly unaffected by changes of temperature, pH and nutritional conditions in order to provide reliable timing. In order to determine which topological principles render the amplitude or period of oscillatory systems robust we perform sensitivity analyses for a chain model as prototype oscillator. The parameters are thereby chosen in an approach based on Monte-Carlo sampling. We examine structural properties as type of feedback, existence of flow of matter between species and kinetics and deduce structural principles leading to robust oscillatory properties. We additionally perform sensitivity analyses for mathematical models of calcium oscillations and circadian oscillations for a great variety of different parameter sets and explain their period robustness behavior with the help of the structural principles found in the prototype oscillator model.