  Let $X, Y$ be Banach spaces and $T : X \to Y$ be a bounded linear operator.
In this paper, we initiate the study of the perturbation problems for bounded
homogeneous generalized inverse $T^h$ and quasi--linear projector generalized
inverse $T^H$ of $T$. Some applications to the representations and
perturbations of the Moore--Penrose metric generalized inverse $T^M$ of $T$ are
also given. The obtained results in this paper extend some well--known results
for linear operator generalized inverses in this field.
