Abstract: By studying the properties of quasi-σ-spaces and quasi-G_δ-diagonals, some conditions on the metrizability of generalized ordered topological spaces and some results around linearly ordered topological spaces, which have quasi-G_δ-diagonals are obtained. These results modify some related results concerning quasi-σ-spaces and quasi-G_δ-diagonals in the literature. The main results are: X is a σ-space if and only if it is a quasi-σ-space; A linearly ordered topological space with a quasi-G_δ-diagonal is a Θ-space.