Method of handling or moving the stitches of a textile article, the method comprising removing the stitches from the needles of a textile machine by with the transferring article is formed at a first station, transferring the article from said first station to a second operating station, said transfer being operated by engaging the said stitches with a plurality of members intended for the removal of same stitches form the needles of the textile machine and transferring said members from said first station to said second station, characterized in that it comprises the reversible transfer of at least one portion of said removal members from a first support or carrier which is being movable from said first and second stations to a second support or carrier intended for temporary retaining the said at least one portion of removal members along with the stitches being removed by them, and/or the reversible transfer of a plurality of members, intended for the temporary retention of the stitches and not involved in the removal of same stitches from said needles, between two movable supports or carriers.