  Non-geometric string backgrounds were proposed to be related to a
non-associative deformation of the space-time geometry. In the flux formulation
of double field theory (DFT), the structure of mathematically possible
non-associative deformations is analyzed in detail. It is argued that on-shell
there should not be any violation of associativity in the effective DFT action.
For imposing either the strong or the weaker closure constraint we discuss two
possible non-associative deformations of DFT featuring two different ways how
on-shell associativity can still be kept.
