A labelling machine (1, 1') for applying labels onto articles intended to contain a pourable product; said labelling machine (1, 1') comprising: - a conveyor configured to advance a plurality of said articles along a transfer path; and - a transfer element, arranged peripherally to said conveyor and configured to receive a sequence of single labels one after the other at a receiving station, to retain said labels onto a lateral surface thereof and to convey said labels, along an advancement direction, towards an application station, at which said labels are, in use, released from said lateral surface and are, in use, fed to said conveyor to be applied onto said articles; - third detection means arranged in a position downstream of said application station; - extraction means for said labels, arranged peripherally to said transfer element, in a position operatively downstream of said third detection means; characterized by comprising second detection means arranged in a position downstream of said receiving station and upstream of said application station, relatively to said advancement direction, and configured to detect a positioning of each label onto said lateral surface and to generate a positioning signal correlated with said positioning of said each label; wherein: said labelling machine (1, 1') further comprises first detection means, arranged peripherally to said transfer element in a position downstream of said application station and upstream of said receiving station, relatively to said advancement direction, and configured to detect the single labels still retained in use, by said lateral surface downstream of said application station and to generate a presence signal correlated with the presence of said labels still retained in use, by said lateral surface downstream of said application station; the third detection means are arranged upstream said first detection means and configured to generate a further presence signal when a label is present onto said lateral surface downstream of said application station and upstream of said first detection means; - the extraction means are arranged in a position operatively upstream of said first detection means, and defining a discard station (D') for said labels; and - said labelling machine (1, 1') further comprises activation means configured to activate said extraction means in response of said further presence signal. - a conveyor configured to advance a plurality of said articles along a transfer path; and - a transfer element, arranged peripherally to said conveyor and configured to receive a sequence of single labels one after the other at a receiving station, to retain said labels onto a lateral surface thereof and to convey said labels, along an advancement direction, towards an application station, at which said labels are, in use, released from said lateral surface and are, in use, fed to said conveyor to be applied onto said articles; - third detection means arranged in a position downstream of said application station; - extraction means for said labels, arranged peripherally to said transfer element, in a position operatively downstream of said third detection means; said labelling machine (1, 1') further comprises first detection means, arranged peripherally to said transfer element in a position downstream of said application station and upstream of said receiving station, relatively to said advancement direction, and configured to detect the single labels still retained in use, by said lateral surface downstream of said application station and to generate a presence signal correlated with the presence of said labels still retained in use, by said lateral surface downstream of said application station; the third detection means are arranged upstream said first detection means and configured to generate a further presence signal when a label is present onto said lateral surface downstream of said application station and upstream of said first detection means; - the extraction means are arranged in a position operatively upstream of said first detection means, and defining a discard station (D') for said labels; and - said labelling machine (1, 1') further comprises activation means configured to activate said extraction means in response of said further presence signal. - the extraction means are arranged in a position operatively upstream of said first detection means, and defining a discard station (D') for said labels; and - said labelling machine (1, 1') further comprises activation means configured to activate said extraction means in response of said further presence signal.