An assembly machine for producing multicomponent cigarettes, each comprising a number of portions, which have a central axis and comprise at least one portion defined by a filter element, and at least another portion defined by an aromatic, preferably tobacco-based, element; the assembly machine comprising: a combining unit for forming groups of portions, each comprising at least two different first portions (3A, 3B, 3C) aligned axially and contacting end to end, and in which the groups of portions travel perpendicularly to their central axis; the combining unit comprises a number of structurally identical feed stations, each for supplying a respective first portion (3A, 3B, 3C) to form the groups of portions; and each feed station comprises an insertion drum, which receives the groups of portions from a preceding feed station or creates the groups of portions, receives respective first portions (3A, 3B, 3C), and inserts the respective first portions (3A, 3B, 3C) into the groups of portions; wherein each group of portions is not wrapped with any sheet of wrapping material in the combining unit; and a first wrapping unit, which receives a succession of groups of portions, aligned axially and contacting end to end, from the combining unit, feeds the groups of portions perpendicularly to their central axis, and winds a single first sheet of wrapping material around the whole circumference of each group of portions; and a second wrapping unit, which receives a succession of groups of portions from the first wrapping unit, feeds the groups of portions perpendicularly to their central axis, and winds a single second sheet of wrapping material around the whole circumference of each group of portions; wherein the second wrapping unit comprises a first portion feed unit for inserting second portions into the groups of portions; the assembly machine being characterized in that the second wrapping unit comprises a hopper containing a mass of second portions, a cutting drum for cutting the second portions transversely to the desired length; and a pickup drum, which withdraws the second portions successively from the hopper and cooperates with the cutting drum. a combining unit for forming groups of portions, each comprising at least two different first portions (3A, 3B, 3C) aligned axially and contacting end to end, and in which the groups of portions travel perpendicularly to their central axis; the combining unit comprises a number of structurally identical feed stations, each for supplying a respective first portion (3A, 3B, 3C) to form the groups of portions; and each feed station comprises an insertion drum, which receives the groups of portions from a preceding feed station or creates the groups of portions, receives respective first portions (3A, 3B, 3C), and inserts the respective first portions (3A, 3B, 3C) into the groups of portions; wherein each group of portions is not wrapped with any sheet of wrapping material in the combining unit; and a first wrapping unit, which receives a succession of groups of portions, aligned axially and contacting end to end, from the combining unit, feeds the groups of portions perpendicularly to their central axis, and winds a single first sheet of wrapping material around the whole circumference of each group of portions; and a second wrapping unit, which receives a succession of groups of portions from the first wrapping unit, feeds the groups of portions perpendicularly to their central axis, and winds a single second sheet of wrapping material around the whole circumference of each group of portions; wherein the second wrapping unit comprises a first portion feed unit for inserting second portions into the groups of portions; the assembly machine being characterized in that the second wrapping unit comprises a hopper containing a mass of second portions, a cutting drum for cutting the second portions transversely to the desired length; and a pickup drum, which withdraws the second portions successively from the hopper and cooperates with the cutting drum.