This paper is concerned with scheduling when the data are not fully knownbefore the execution. In that case computing a complete schedule off-linewith estimated data may lead to poor performances. Some flexibility must beadded to the scheduling process. We propose to start from a partial schedule and to postpone the complete scheduling until execution, thus introducing what we call a stabilizationscheme. This is applied to the m machine problem with communicationdelays: in our model an estimation of the delay is known at compile time; but disturbances due to network contention, link failures, ... may occur at execution time. Hence the processor assignment and a partial sequencing on each processor are determined off-line. Some theoreticalresults for tree-like precedence constraints and an experimental study show the interest of this approach compared with fully on-line scheduling.