A one-dimensional tight-binding model on a spatially periodic lattice of length N, with quasiperiodic potential strength given by the Fibonacci sequence, is investigated numerically. We elucidate the N-dependence of the resistence and the nature of the wave functions. For energies belonging to the spectrum, the results provide strong evidence for algebraic localization and algebraic N-dependence of the resistance, with a distribution of exponents. Implications for quantum chaos are also discussed. © 1987 Springer-Verlag.