Investigations of the losses in multifilamentary composite conductors which result from the simultaneous change of the external field B
eand transport current I are presented. The total loss is best characterized by a maximum normalized transport current i
m= I
m/I
c(I
c= critical current) and a dimensionless field-change rate

, where τ is the relaxation time of the coupling current and B
pis the full-penetration field of a solid superconductor equivalent to the multifilamentary composite. For

, the composite conductor behaves like a solid and a saturation effect occurs in the loss. The characteristic feature of the composite appears only for

. The increase in losses arising from the non-zero transport current theoretically, is not larger than about 30 percent. For practical calculations, the experimental results over a wide range of β and i
magree well with the theory.