Process for catalytic hydrotreatment of a heavy hydrocarbon-based feedstock, in the presence of hydrogen, comprising a prior hydrodemetallation step by means of at least two fixed bed switchable reactors, each comprising at least one catalytic bed, which are used cyclically according to the following steps: a) a step in which at least two reactors are used in series in descending flow mode until a pressure drop threshold Dpi having a value of between 20 and 70% of the maximum admissible pressure drop DPmax is reached, b) a step of reversing the direction of the flow and of placing said at least two reactors in parallel until the maximum admissible pressure drop DPmax is reached, c) a step during which the first reactor brought into contact with the feedstock in step a) is bypassed and the catalyst that it contains is regenerated and/or replaced with fresh catalyst, the direction of the flow is modified and only the reactor(s) not yet blocked operate in descending flow mode, d) a step during which said at least two reactors are used in series, the reactor of which the catalyst was regenerated during the preceding step being reconnected and said step being continued until a pressure drop threshold Dpi having a value of between 20 and 70% of the maximum admissible pressure drop DPmax is reached, e) a step of reversing the direction of the flow and of placing the two reactors in parallel, until the maximum admissible pressure drop DPmax is reached, f) a step during which the second reactor brought into contact with the feedstock in step a) is bypassed and the catalyst that it contains is regenerated and/or replaced with fresh catalyst, the direction of the flow is modified and only the reactor(s) not yet blocked operate in descending flow mode; said steps a), b), c), d), e) and f) possibly being repeated cyclically in this order. a) a step in which at least two reactors are used in series in descending flow mode until a pressure drop threshold Dpi having a value of between 20 and 70% of the maximum admissible pressure drop DPmax is reached, b) a step of reversing the direction of the flow and of placing said at least two reactors in parallel until the maximum admissible pressure drop DPmax is reached, c) a step during which the first reactor brought into contact with the feedstock in step a) is bypassed and the catalyst that it contains is regenerated and/or replaced with fresh catalyst, the direction of the flow is modified and only the reactor(s) not yet blocked operate in descending flow mode, d) a step during which said at least two reactors are used in series, the reactor of which the catalyst was regenerated during the preceding step being reconnected and said step being continued until a pressure drop threshold Dpi having a value of between 20 and 70% of the maximum admissible pressure drop DPmax is reached, e) a step of reversing the direction of the flow and of placing the two reactors in parallel, until the maximum admissible pressure drop DPmax is reached, f) a step during which the second reactor brought into contact with the feedstock in step a) is bypassed and the catalyst that it contains is regenerated and/or replaced with fresh catalyst, the direction of the flow is modified and only the reactor(s) not yet blocked operate in descending flow mode; said steps a), b), c), d), e) and f) possibly being repeated cyclically in this order.