It is shown that, under minor additional assumptions, the standard parabolic subgroups of a Chevalley group G_ρ(Φ, R) of twisted type Φ=A_l, l odd, D_l, E₆ over a commutative semilocal ring R with involution ρ are in one-to-one correspondence with the ρ-invariant parabolic nets of ideals of R of type Φ, i.e., with the sets[Figure not available: see fulltext.], of ideals σ_α of R such that: (l)[Figure not available: see fulltext.][Figure not available: see fulltext.] whenever[Figure not available: see fulltext.]; (2)ρσ_α=σ_ρα for all α; (3) σ_α=R for α > 0. For Chevalley groups of normal types, analogous results were obtained in Ref. Zh. Mat. 1976, 10A151; 1977, 10A 301; 1978, 6A476.