Hysteresis losses in a twisted filamentary superconducting wire are calculated for various cases corresponding to complete penetration of the magnetic field into the wire, shielding of the field by the supercurrents, and shielding due to eddy currents. In general, the wire may be divided into two regions; an outer saturated layer which tends to behave at the higher frequencies like a solid superconductor and the interior where the average parallel electric field vanishes and the wire behaves like a collection of individual filaments.