A subalgebra B of a Leibniz algebra L is called a weak c-ideal of
L if there is a subideal C of L such that L = B + C and B ∩ C ⊆ BL
where BL is the largest ideal of L contained in B. This is analogous
to the concept of a weakly c-normal subgroup, which has been studied
by a number of authors. We obtain some properties of weak c-ideals
and use them to give some characterisations of solvable and supersolvable Leibniz algebras generalising previous results for Lie algebras. We
note that one-dimensional weak c-ideals are c-ideals, and show that a
result of Turner classifying Leibniz algebras in
which every one-dimensional subalgebra is a c-ideal is false for general
Leibniz algebras, but holds for symmetric ones.