The current ramp-up phase for the ITER hybrid scenario is analyzed with the CRONOS integrated modelling suite. The simulations presented in this paper show that the heating systems available at ITER allow, within the operational limits, the attainment of a hybrid q profile at the end of the current ramp-up. A reference ramp-up scenario is reached by a combination of NBI, ECCD (UPL) and LHCD. A heating scheme with only NBI and ECCD can also reach the target q profile; however, LHCD can play a crucial role in reducing the flux consumption during the ramp-up phase. The optimum heating scheme depends on the chosen transport model, and on assumptions on parameters like n e peaking, edge T e,i and Z eff. The sensitivity of the current diffusion on parameters that are not easily controlled, shows that development of real time control is important to reach the target q profile. A first step in that direction has been indicated in this paper. Minimizing resistive flux consumption and optimizing the q profile turn out to be conflicting requirements. A trade-off between these two requirements has to be made. In this paper it is shown that fast current ramp with L-mode current overshoot is at the one extreme, i.e. optimum q profile at the cost of increased resistive flux consumption, whereas early H-mode transition is at the other extreme.