Feeding unit for feeding a tissue converting machine for converting a web (W1, W2) of two-layer tissue, the feeding unit comprising: - support means for rotatably supporting a first reel of two-layer tissue web and a second reel of two-layer tissue web for rotation about respective axes of rotation (x1, x2); - cutting means (32, 42) for cutting the two layers (L1_1, L2_1) of the tissue web of one of said first and second reels (R1, R2), namely the reel in use, said cutting means (32, 42) being configured to cut the two layers (L1_1, L2_1) of the tissue web along two cut lines spaced from each other in the longitudinal direction of the web; - joining means (44_1, 44_2) for joining each of the two layers (L1_2, L2_2) of the tissue web of the other one of said first and second reels (R1, R2), namely the new reel, to a respective layer (L1_1, L2_1) of the tissue web of the reel in use; and - tissue web accumulation means for accumulating a given amount of tissue web downstream of the cutting means (32, 42) and of the joining means (44_1, 44_2) so as to ensure that the machine is fed with the tissue web while the portion of tissue web on which the cutting means (32, 42) and the joining means (44_1, 44_2) act is kept temporarily still to allow cutting of the two layers (L1_1, L2_1) of the tissue web in use and joining of these layers to the two layers (L1_2, L2_2) of the new tissue web, wherein said cutting means (32, 42) comprise a first cutting member for cutting the inner layer (L1_1) of the tissue web in use and a pair of second cutting members which are placed on opposite sides of the first cutting member with respect to a plane parallel to the web in use and are arranged to cut the outer layer (L2_1) of the tissue web in use, said second cutting members being positioned at a distance from said first cutting member in the longitudinal direction of the tissue web in use, wherein said first cutting member is placed downstream of said second cutting members with respect to the feeding direction of the tissue web in use, and wherein each of said second cutting members comprises a separating element adapted to be inserted between the two layers (L1_1, L2_1) of the tissue web in use to keep said layers (L1_1, L2_1) detached from each other along a side edge of the tissue web in use. - support means for rotatably supporting a first reel of two-layer tissue web and a second reel of two-layer tissue web for rotation about respective axes of rotation (x1, x2); - cutting means (32, 42) for cutting the two layers (L1_1, L2_1) of the tissue web of one of said first and second reels (R1, R2), namely the reel in use, said cutting means (32, 42) being configured to cut the two layers (L1_1, L2_1) of the tissue web along two cut lines spaced from each other in the longitudinal direction of the web; - joining means (44_1, 44_2) for joining each of the two layers (L1_2, L2_2) of the tissue web of the other one of said first and second reels (R1, R2), namely the new reel, to a respective layer (L1_1, L2_1) of the tissue web of the reel in use; and - tissue web accumulation means for accumulating a given amount of tissue web downstream of the cutting means (32, 42) and of the joining means (44_1, 44_2) so as to ensure that the machine is fed with the tissue web while the portion of tissue web on which the cutting means (32, 42) and the joining means (44_1, 44_2) act is kept temporarily still to allow cutting of the two layers (L1_1, L2_1) of the tissue web in use and joining of these layers to the two layers (L1_2, L2_2) of the new tissue web, wherein said cutting means (32, 42) comprise a first cutting member for cutting the inner layer (L1_1) of the tissue web in use and a pair of second cutting members which are placed on opposite sides of the first cutting member with respect to a plane parallel to the web in use and are arranged to cut the outer layer (L2_1) of the tissue web in use, said second cutting members being positioned at a distance from said first cutting member in the longitudinal direction of the tissue web in use, wherein said first cutting member is placed downstream of said second cutting members with respect to the feeding direction of the tissue web in use, and wherein each of said second cutting members comprises a separating element adapted to be inserted between the two layers (L1_1, L2_1) of the tissue web in use to keep said layers (L1_1, L2_1) detached from each other along a side edge of the tissue web in use.