The paper present the development of a closed-loop control algorithm for a 2-stage turbocharging system aiming to optimize fuel consumption, by minimizing pumping losses, and transient response, by minimizing time to reach a charging pressure set-point. The task is challenging, as the two objectives require counteracting management of low and high pressure turbocharging stage and the relevant turbine control device, i.e. waste-gate position. The subject is interesting, as the number of application of turbocharging technique to gasoline engines is growing, aiming at the reduction of fuel consumption and CO2 emissions while improving performances. Anyway, the paper is not acceptable in its present version, as different aspects need to be clarified. The term “over-actuation” is widely used in the manuscript. Though its meaning is arguable, a definition should be included. It must be specified the relationship between the waste-gate actuation signals and the relevant waste-gate positions, that is, for example, if uwg,hp=100% corresponds to a complete closure of the waste-gate of the high pressure turbine. Lines 98-105 and 117-124: text is exactly the same. Figure 3: a better choice of colors representing the different levels of engine speed should be done to improve the readability. The indication of graph for high and low pressure stage should be clearer, as it can only be derived by the mass reported on X axis. Moreover, no indication on waste-gate combinations can be observed in the figure. This also prevent to fully understand the statement at line 151. Line 155: the discussed figure is number 4, not 6. Line 163: the statement should be clarified in terms of waste-gate positions (closed-opened) of the two stages. Line 164: the statement “… this hold true even for small mass flows” should be proved with an example from fig.4. Figure 5: a better explanation has to be included. The step input start after 1 s, this should be specified when giving values of t95 (lines 180 and 181). What do the two curves represent? What is Dpchar, norm? There is probably an error in the indication of the parameter shown in the last two graphs, as one should be the actuation signal of the low pressure stage waste-gate. Terms included in equations 17, 23 and 29 should be explained, taking also into account that they are not included in abbreviations and indices. Line 245: what does “sates” mean? Line 255: please check the statement, as the controller reducing pumping losses should mostly use the low pressure stage. Figure 7: as in figure 5, there is probably an error in the indication of the parameter shown in the last two graphs, as one should be the actuation signal of the low pressure stage waste-gate. More important, following the text explanation (lines 259-264), the third strategy, optimizing both the objectives, should reach strategy 1 after the transient in order to reduce fuel consumption. It is not clear (and is misleading, observing the figure) why it becomes strategy 2 in figure caption. The presented transient response is a quite simple case study: what about the controller behavior on a driving cycle or in real world conditions?