Functional　data　are　infinite-dimensional　statistical　objects　which　pose　significant　challenges　to　both　theorists　and　practitioners.　Both　parametric　and　nonparametric　regressions　have　received　attention　in　the　functional　data　analysis　literature.　However,　the　former　imposes　stringent　constraints　while　the　latter　suffers　from　logarithmic　convergence　rates.　In　this　article,　we　consider　two　popular　sufficient　dimension　reduction　methods　in　the　context　of　functional　data　analysis,　which,　if　desired,　can　be　combined　with　low-dimensional　nonparametric　regression　in　a　later　step.　In　computation,　predictor　processes　and　index　vectors　are　approximated　in　finite　dimensional　spaces　using　the　series　expansion　approach.　In　theory,　the　basis　used　can　be　either　fixed　or　estimated,　which　include　both　functional　principal　components　and　B-spline　basis.　Thus　our　study　is　more　general　than　previous　ones.　Numerical　results　from　simulations　and　a　real　data　analysis　are　presented　to　illustrate　the　methods.　(C)　2013　Elsevier　Inc.　All　rights　reserved.