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We examine numerically the effect of quasiperiodicity in the nature of the states in Fibonacci semiconductor superlattices by means of the transfer matrix formalism. We are interested in the GaAs/Al x Ga1 − x As layers, having identical thickness, where the aluminium concentration x takes, two different values. We have found that each miniband of the periodic superlattice splits in several sub-minibands, that is small minigaps appear. We demonstrate that the origin of these small inner minigaps is due to the loss of long-range quantum coherent of the electrons wave. The corresponding electronic spectrum shows a high fragment. The states having transmission coefficient close to zero in the minibands can be viewed as consisting of singular localised states.