Using the dynamical-map method, we study the electronic properties for diagonal and off-diagonal tight-binding model in a class of one-dimensional quasiper-iodic systems. These systems are associated with the generalized Fibonacci sequences S∞ given by the recursion relation Sl+1=Sl2j-1Sl-12i for l≥1 with two initial sequences S0 and S1, where i and j are positive integers. Analytical treatments show that the extended electronic states for these one-dimensional quasiperiodic sequences really exist.