An apparatus for tying a wire (46, 52) around one or more objects such as concrete reinforcing bars (2) is disclosed. It comprises means for passing the wire (46, 52) in a loop around the bars and a rotatable head 4 for twisting the ends of the loop together. The head (4) has at least one gripping means such as a variable force clutch (32) for gripping the wire, the gripping means being adapted to provide a variable gripping force so as to apply a predetermined tension to the wire during at least a first phase of twisting. Also disclosed is pre-feeding the wire between tying operations; conditioning the surface of the wire; and using the electrical conductivity of the reinforcing bars to verify that the bars are present before tying.