  We introduce a notion of $(S+N)$-triangular operators in the Hilbert space
using some basic ideas from triangular representation theory. Our notion
generalizes the well-known notion of the spectral operators so that many
properties of the $(S+N)$-triangular operators coincide with those of spectral
operators. At the same time we show that wide classes of operators are
$(S+N)$-triangular.
