Let X 1 ; :::; X n be an i.i.d. sample of random curves, viewed as Hilbert space valued random elements, with mean curve m: An asymptotic test of m = m 0 vs m 6 = m 0 is proposed, when m 0 is a …xed known function. The test statistics converges under very mild assumptions and relies on the pseudo-inversion of the covariance operator (leading to a non standard inverse problem). The power against local alternatives is investigated.