Based on Euler equations, an implicit time-dependent method is applied for the calculation of the transonic blade-to-blade flows with strong shock waves. The ntmerical method is based ' on a fully implicit time difference scheme. The stabilizing correction method is utilised as an ADI sequence to break down the two dimensional operator into two operators. These opera-tors are selected so that at each time step the variables are determined independently of each other. The work presented here is an adaptation, to turbomachinery flows, of the basic method previously publicized and well applied in the internal nozzle flow. The purpose of this paper is to examine the ability of this method to predict the blade-to-blade transonic flow with strong shock waves. Detailed studies of the grid system and corresp-onding problems related to the boundary (inlet,exit and perio-dicity) conditions. Results are presented for the ECDEV tran-sonic compressor cascade with prescribed pressure ratio and with a strong passage shock. The results obtained are compared with those obtained by an explicit method utilised at ONERA - FRANCE.