Summary: We study Lie ideals in two classes of triangular operator algebras: nest algebras and triangular UHF algebras. Our main results show that if \({\mathfrak L}\) is a closed Lie ideal of the triangular operator algebra \({\mathcal A}\), then there exist a closed associative ideal \({\mathcal K}\) and a closed subalgebra \({\mathfrak D}_{\mathcal K}\) of the diagonal \({\mathcal A}\cap{\mathcal A}^*\) so that \({\mathcal K}\subseteq{\mathfrak L}\subseteq{\mathcal K}+ {\mathfrak D}_{\mathcal K}\).