We consider the Hubert transform and maximal function associated to a curve Γ(t) -(t, 72(ί),... , J n (t)) in E n . It is well-known that for a plane convex curve Γ(t) = (t,j(t)) these operators are bounded on L p , 1 < p < 00, if 7' doubles. We give an n-dimensional analogue, n > 2, of this result.