  We consider the topological defect lines commuting with the spectral flow and
the $\mathcal{N}=(4,4)$ superconformal symmetry in two dimensional non-linear
sigma models on K3. By studying their fusion with boundary states, we derive a
number of general results for the category of such defects. We argue that while
for certain K3 models infinitely many simple defects, and even a continuum, can
occur, at generic points in the moduli space the category is actually trivial,
i.e. it is generated by the identity defect. Furthermore, we show that if a K3
model is at the attractor point for some BPS configuration of D-branes, then
all topological defects have integral quantum dimension. We also conjecture
that a continuum of topological defects arises if and only if the K3 model is a
(possibly generalized) orbifold of a torus model. Finally, we test our general
results in a couple of examples, where we provide a partial classification of
the topological defects.
