Apparatus for electrically connecting photovoltaic cells in series, which comprises: - a support structure provided with an advancement lane extended between an inlet station and an outlet station; - a first conveyor belt, which is mounted on said support structure along said advancement lane, is provided with a first forward section susceptible of receiving, at said inlet station, multiple photovoltaic cells in sequence and multiple filiform electrical conductors arranged on at least one face of each of said photovoltaic cells, and is actuatable in order to make said first forward section advance according to an advancement direction in order to convey said photovoltaic cells along said advancement lane; - a welding station, which is arranged along said advancement lane between said inlet station and said outlet station, is crossed by the first forward section of said first conveyor belt, and is provided with first heating means actuatable in order to at least partially melt said electrical conductors so to weld said electrical conductors to said photovoltaic cells; - a second conveyor belt, which is mounted on said support structure along said advancement lane and arranged above said first conveyor belt, is provided with a second forward section passing at least through said welding station and placed facing the first forward section of said first conveyor belt, delimiting with said first forward section an advancement path passing at least through said welding station, and is actuatable in order to make said second forward section advance in said advancement direction in order to drive said photovoltaic cells and said electrical conductors along said advancement path between said first forward section and said second forward section; wherein the first forward section of said first conveyor belt is provided with an upper face facing the second forward section of said second conveyor belt, and with a lower face facing in opposite direction with respect to said upper face; said apparatus being characterized in that said first conveyor belt is provided with through holes susceptible of being crossed by the air; wherein said apparatus comprises suction means, which are arranged along said advancement lane at least at said advancement path and are provided with at least one suction section, which is arranged at least at said welding station below the lower face of the first forward section of said first conveyor belt and is in fluid communication with said advancement path by means of the through holes of said first conveyor belt, in order to create a depression within said advancement path, bringing the second forward section of said second conveyor belt to press on the first forward section of said first conveyor belt at least at said welding station. - a support structure provided with an advancement lane extended between an inlet station and an outlet station; - a first conveyor belt, which is mounted on said support structure along said advancement lane, is provided with a first forward section susceptible of receiving, at said inlet station, multiple photovoltaic cells in sequence and multiple filiform electrical conductors arranged on at least one face of each of said photovoltaic cells, and is actuatable in order to make said first forward section advance according to an advancement direction in order to convey said photovoltaic cells along said advancement lane; - a welding station, which is arranged along said advancement lane between said inlet station and said outlet station, is crossed by the first forward section of said first conveyor belt, and is provided with first heating means actuatable in order to at least partially melt said electrical conductors so to weld said electrical conductors to said photovoltaic cells; - a second conveyor belt, which is mounted on said support structure along said advancement lane and arranged above said first conveyor belt, is provided with a second forward section passing at least through said welding station and placed facing the first forward section of said first conveyor belt, delimiting with said first forward section an advancement path passing at least through said welding station, and is actuatable in order to make said second forward section advance in said advancement direction in order to drive said photovoltaic cells and said electrical conductors along said advancement path between said first forward section and said second forward section; wherein the first forward section of said first conveyor belt is provided with an upper face facing the second forward section of said second conveyor belt, and with a lower face facing in opposite direction with respect to said upper face; said apparatus being characterized in that said first conveyor belt is provided with through holes susceptible of being crossed by the air; wherein said apparatus comprises suction means, which are arranged along said advancement lane at least at said advancement path and are provided with at least one suction section, which is arranged at least at said welding station below the lower face of the first forward section of said first conveyor belt and is in fluid communication with said advancement path by means of the through holes of said first conveyor belt, in order to create a depression within said advancement path, bringing the second forward section of said second conveyor belt to press on the first forward section of said first conveyor belt at least at said welding station.