The invention refers to a teatcup part and a teatcup to be attached to a teatof an animal. The teatcup includes the teatcup part (1) and a connection part(2). The teatcup part is disengageably mountable to the connection part. Theteatcup part (1) includes a shell (3) and a teatcup liner (4) having an upperopening (5) and a lower opening (6). The liner forms an inner space (11) forreceiving the teat through the upper opening and a pulsation chamber (12)between the liner and the shell. The connection part includes a milk-discharging member for the discharge of milk from the teatcup, and a milkchannel (35) extending between the lower opening of the inner space of theliner and the milk-discharging member. The connection part also includes apulse-supplying member for the supply of a pulsating pressure to the pulsationchamber, and a pulse channel extending between the pulsation chamber and thepulse-supplying member.
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