  We study the relaxation for growing interfaces in quenched disordered media.
We use a directed percolation depinning model introduced by Tang and Leschhorn
for 1+1-dimensions. We define the two-time autocorrelation function of the
interface height C(t',t) and its Fourier transform. These functions depend on
the difference of times t-t' for long enough times, this is the steady-state
regime. We find a two-step relaxation decay in this regime. The long time tail
can be fitted by a stretched exponential relaxation function. The relaxation
time is proportional to the characteristic distance of the clusters of pinning
cells in the direction parallel to the interface and it diverges as a power
law. The two-step relaxation is lost at a given wave length of the Fourier
transform, which is proportional to the characteristic distance of the clusters
of pinning cells in the direction perpendicular to the interface. The stretched
exponential relaxation is caused by the existence of clusters of pinning cells
and it is a direct consequence of the quenched noise.
