Portable dispenser for a plurality of fluid or pasty products, comprising: - a dispenser body; - a dispensing head which is guided in rotation and fixed in translation relative to the dispenser body about a reference axis of the dispenser, the dispensing head comprising at least one dispensing opening, the dispensing opening preferably being aligned with the reference axis of the dispenser; - a pumping assembly comprising at least one first pump (16A, 16B, 16C) and at least one second pump (16A, 16B, 16C), the first pump (16A, 16B, 16C) comprising a tubular spraying nozzle (54A, 54B, 54C) defining a first ejection axis (200A, 200B, 200C) which is fixed relative to the dispenser body and is parallel to the reference axis of the dispenser, the spraying nozzle (54A, 54B, 54C) of the first pump (16A, 16B, 16C) being translatable relative to the dispenser body in parallel with the first ejection axis (200A, 200B, 200C), the second pump (16A, 16b, 16C) comprising a tubular spraying nozzle (54A, 54B, 54C) defining a second ejection axis (200A, 200B, 200C) which is fixed relative to the dispenser body and is parallel to the first ejection axis (200A, 200B, 200C), the spraying nozzle (54A, 54B, 54C) of the second pump (16A, 16B, 16C) being translatable relative to the dispenser body in parallel with the second ejection axis (200A, 200B, 200C), - a kinematic connection between the dispensing head and the spraying nozzles of the first pump and second pump (54A, 54B, 54C) for converting a rotational movement without translation of the dispensing head relative to the dispenser body about the reference axis of the dispenser into a translational movement without rotation of the spraying nozzles of the first pump and second pump (54A, 54B, 54C) relative to the dispenser body in parallel with the reference axis of the dispenser, the kinematic connection comprising a pusher positioned between the pumping assembly and the dispensing head, the pusher being connected to the dispenser body by a sliding connection (58, 98) which is capable of guiding a translational movement without rotation of the pusher relative to the dispenser body, the pusher being capable of bearing against the spraying nozzle (54A, 54B, 54C) of the first pump (16A, 16B, 16C) and against the spraying nozzle (54A, 54B, 54C) of the second pump (16A, 16B, 16C) when the dispensing head rotates relative to the dispenser body about the reference axis of the dispenser, the pusher comprising at least a first dispensing duct (96A, 96B, 96C) for channeling a first fluid leaving the spraying nozzle (54A, 54B, 54C) of the first pump (16A, 16B, 16C) toward the dispensing opening, and a second dispensing duct (96A, 96B, 96C) for channeling a fluid leaving the spraying nozzle (54A, 54B, 54C) of the second pump (16A, 16B, 16C) toward the dispensing opening. - a dispenser body; - a dispensing head which is guided in rotation and fixed in translation relative to the dispenser body about a reference axis of the dispenser, the dispensing head comprising at least one dispensing opening, the dispensing opening preferably being aligned with the reference axis of the dispenser; - a pumping assembly comprising at least one first pump (16A, 16B, 16C) and at least one second pump (16A, 16B, 16C), the first pump (16A, 16B, 16C) comprising a tubular spraying nozzle (54A, 54B, 54C) defining a first ejection axis (200A, 200B, 200C) which is fixed relative to the dispenser body and is parallel to the reference axis of the dispenser, the spraying nozzle (54A, 54B, 54C) of the first pump (16A, 16B, 16C) being translatable relative to the dispenser body in parallel with the first ejection axis (200A, 200B, 200C), the second pump (16A, 16b, 16C) comprising a tubular spraying nozzle (54A, 54B, 54C) defining a second ejection axis (200A, 200B, 200C) which is fixed relative to the dispenser body and is parallel to the first ejection axis (200A, 200B, 200C), the spraying nozzle (54A, 54B, 54C) of the second pump (16A, 16B, 16C) being translatable relative to the dispenser body in parallel with the second ejection axis (200A, 200B, 200C), - a kinematic connection between the dispensing head and the spraying nozzles of the first pump and second pump (54A, 54B, 54C) for converting a rotational movement without translation of the dispensing head relative to the dispenser body about the reference axis of the dispenser into a translational movement without rotation of the spraying nozzles of the first pump and second pump (54A, 54B, 54C) relative to the dispenser body in parallel with the reference axis of the dispenser, the kinematic connection comprising a pusher positioned between the pumping assembly and the dispensing head, the pusher being connected to the dispenser body by a sliding connection (58, 98) which is capable of guiding a translational movement without rotation of the pusher relative to the dispenser body, the pusher being capable of bearing against the spraying nozzle (54A, 54B, 54C) of the first pump (16A, 16B, 16C) and against the spraying nozzle (54A, 54B, 54C) of the second pump (16A, 16B, 16C) when the dispensing head rotates relative to the dispenser body about the reference axis of the dispenser, the pusher comprising at least a first dispensing duct (96A, 96B, 96C) for channeling a first fluid leaving the spraying nozzle (54A, 54B, 54C) of the first pump (16A, 16B, 16C) toward the dispensing opening, and a second dispensing duct (96A, 96B, 96C) for channeling a fluid leaving the spraying nozzle (54A, 54B, 54C) of the second pump (16A, 16B, 16C) toward the dispensing opening.