Apparatus for manufacturing a product, in particular a cosmetic product, comprising a mixing machine comprising - a removable receiving device comprising - a first reception location, configured to receive a first capsule containing a first formulation, - a second reception location, configured to receive a second capsule containing a second formulation, the two capsules (3, 4) able to be fluidically coupled, - a first actuating face of the receiving device, authorising a transfer of pressure onto the first capsule, - a second actuating face of the receiving device, opposite the first, authorising a transfer of pressure into the second capsule, - a retaining stop (9.6) extending as a protrusion. - a support defining a receiving casing, able to receive the receiving device - an actuating system, which is movable inside the receiving casing to exert a pressure on the receiving device and/or on the first and/or second capsule (3, 4), - a retaining mechanism which is movable relative to the support, disposed facing the retaining stop (9.6) when said receiving device is inserted into the apparatus, the retaining mechanism being configured ∗ in an insertion position, to authorise the insertion and removal of the receiving device from the receiving casing, and ∗ in a retaining position, be able to abut against the retaining stop (9.6) in a blocked position so as to block the removal of the receiving device from the receiving casing, - a removable receiving device comprising - a first reception location, configured to receive a first capsule containing a first formulation, - a second reception location, configured to receive a second capsule containing a second formulation, the two capsules (3, 4) able to be fluidically coupled, - a first actuating face of the receiving device, authorising a transfer of pressure onto the first capsule, - a second actuating face of the receiving device, opposite the first, authorising a transfer of pressure into the second capsule, - a retaining stop (9.6) extending as a protrusion. - a first reception location, configured to receive a first capsule containing a first formulation, - a second reception location, configured to receive a second capsule containing a second formulation, the two capsules (3, 4) able to be fluidically coupled, - a first actuating face of the receiving device, authorising a transfer of pressure onto the first capsule, - a second actuating face of the receiving device, opposite the first, authorising a transfer of pressure into the second capsule, - a retaining stop (9.6) extending as a protrusion. - a support defining a receiving casing, able to receive the receiving device - an actuating system, which is movable inside the receiving casing to exert a pressure on the receiving device and/or on the first and/or second capsule (3, 4), - a retaining mechanism which is movable relative to the support, disposed facing the retaining stop (9.6) when said receiving device is inserted into the apparatus, the retaining mechanism being configured ∗ in an insertion position, to authorise the insertion and removal of the receiving device from the receiving casing, and ∗ in a retaining position, be able to abut against the retaining stop (9.6) in a blocked position so as to block the removal of the receiving device from the receiving casing, ∗ in an insertion position, to authorise the insertion and removal of the receiving device from the receiving casing, and ∗ in a retaining position, be able to abut against the retaining stop (9.6) in a blocked position so as to block the removal of the receiving device from the receiving casing,