Critical magnetic fields parallel and perpendicular to the planes of quasiperiodic superconducting Fibonacci multilayers (ML) consisting of vanadium and zirconium are measured. The temperature dependence of the parallel critical fieldHc∥displays two crossovers. TheHc∥(T)dependence is of square-root type in the vicinity of the transition temperatureTcand linear at low temperatures. Between these temperature intervals, the dependence follows a power law:Hc∥∼(1−T/Tc)&agr;,&agr;=0,78±0,02.The complex nature of this dependence can be explained in the framework of the Ginzburg–Landau theory for a quasiperiodic ML, as well as by the scaling theory for fractal multilayers which takes into account the different structure length scales in the case of ML with a complex sequence of layers. ©1998 American Institute of Physics.