The design of aperiodic reflecting multilayer (ML) structures for attosecond physics in the extreme ultraviolet spectral region is presented. An optimization procedure based on “evolutive strategy” has been developed in order to get coating structures reflecting high photon fluxes in ultrashort duration pulses. The MLs are designed for a specific \left(75–105\text{\hspace{0.17em} eV}\right) spectral interval with suitable reflectance and phase characteristics, in particular high total spectral reflectivity coupled with very wide bandwidth, spectral phase compensation, and amplitude reshaping. Furthermore, to take into account manufacturing tolerances, solutions stable with respect to random layer thickness variations are selected. To test the reliability of the proposed design procedure, examples of Mo∕Si ML structures designed to reflect ultrashort pulses with different amplitude profiles and phase behavior are considered. The performances of the various structures are analyzed.