  A relationship between the asymptotic and lower-degree conservation laws in
(non-)linear gauge theories is considered. We show that the true algebraic
structure underlying asymptotic charges is that of Leibniz rather than Lie. The
Leibniz product is defined through the derived bracket construction for the
natural Poisson brackets and the BRST differential. Only in particular, though
not rare, cases that the Poisson brackets of lower-degree conservation laws
vanish modulo central charges, the corresponding Leibniz algebra degenerates
into a Lie one. The general construction is illustrated by two standard
examples: Yang-Mills theory and Einstein's gravity.
