Machine for producing packages of folded or interfolded laminar products made of paper material, in particular packages of napkins, tissues, towels, or similar products, said machine comprising a support frame configured to support: - a feeding group configured to feed a first and a second web of paper (5a,5b) respectively along a first and a second predetermined feeding direction (105a, 105b); - a cutting group configured to cut said first and second webs of paper (5a,5b), respectively, into a first and a second plurality of sheets of paper of predetermined length; - a folding or interfolding group equipped with a first and a second counter-rotating folding roll (31,32) adapted to rotate about respective longitudinal rotation axes (131,132) and configured to fold or interfold said first and second pluralities of sheets of paper at a folding or interfolding zone, in such a way to obtain a stack of sheets folded or interfolded according to a predetermined folding or interfolding configuration, said cutting group and said folding or interfolding group being mounted on a same support body configured to move between an assembled position in which is adapted to be supported by said support frame, and a disassembled position, in which is not adapted to be supported by said support frame; - a displacement group configured to displace said support body between said assembled position and said disassembled position; said machine being characterized in that said displacement group is configured to displace said support body from said assembled position to said disassembled position by lifting said support body from said support frame, and to displace said support body from said disassembled position to said assembled position by lowering said support body on said support frame, and in that said displacement group and said support body are provided with respective engagement portions (58,118) configured to engage with each other in such a way to allow said displacement group to displace said support body between said assembled position and said disassembled position with respect to said support frame. - a feeding group configured to feed a first and a second web of paper (5a,5b) respectively along a first and a second predetermined feeding direction (105a, 105b); - a cutting group configured to cut said first and second webs of paper (5a,5b), respectively, into a first and a second plurality of sheets of paper of predetermined length; - a folding or interfolding group equipped with a first and a second counter-rotating folding roll (31,32) adapted to rotate about respective longitudinal rotation axes (131,132) and configured to fold or interfold said first and second pluralities of sheets of paper at a folding or interfolding zone, in such a way to obtain a stack of sheets folded or interfolded according to a predetermined folding or interfolding configuration, said cutting group and said folding or interfolding group being mounted on a same support body configured to move between an assembled position in which is adapted to be supported by said support frame, and a disassembled position, in which is not adapted to be supported by said support frame; - a displacement group configured to displace said support body between said assembled position and said disassembled position;