  We describe four different types of the ${\cal N} = (4,4)$ twisted
supermultiplets in two-dimensional ${\cal N} = (2,2)$ superspace ${\bf
R}^{1,1|2,2}$. All these multiplets are presented by a pair of chiral and
twisted chiral superfields and differ in the transformation properties under an
extra hidden ${\cal N} = (2,2)$ supersymmetry. The sigma model ${\cal N} =
(2,2)$ superfield Lagrangians for each type of the ${\cal N} = (4,4)$ twisted
supermultiplets are real functions subjected to some differential constraints
implied by the hidden supersymmetry. We prove that the general sigma model
action, with all types of ${\cal N} = (4,4)$ twisted multiplets originally
included, is reduced to a sum of sigma model actions for separate types. An
interaction between the multiplets of different sorts is possible only through
the appropriate mass terms, and only for those multiplets which belong to the
same `self-dual' pair.
