Let N be the set of nonnegative integers and A be a 2-torsion free triangular algebra over a commutative ring R . In the present paper, under some lenient assumptions on A , it is proved that if Δ = { δ n } n ∈ ℕ is a sequence of R -linear mappings δ n : A → A satisfying δ n ( [ [ x , y ] , z ] ) = ∑ i + j + k = n [ [ δ i ( x ) , δ j ( y ) ] , δ k ( z ) ] for all x , y , z ∈ A with x y = 0 (resp. x y = p , where p is a nontrivial idempotent of A ), then for each n ∈ ℕ , δ n = d n + τ n ; where d n : A → A is R -linear mapping satisfying d n ( x y ) = ∑ i + j = n d i ( x ) d j ( y ) for all x , y ∈ A , i.e. D = { d n } n ∈ ℕ is a higher derivation on A and τ n : A → Z ( A ) (where Z ( A ) is the center of A ) is an R -linear map vanishing at every second commutator [ [ x , y ] , z ] with xy=0 (resp. x y = p ).

Keywords: triangular algebra, Lie higher derivation, Lie triple higher derivation