Conserved Quasilocal Quantities and General Covariant Theories in Two Dimensions

General matterless–theories in 1+1 dimensions include dilaton gravity, Yang–Mills theory as well as non–Einsteinian gravity with dynamical torsion and higher power gravity, and even models of spherically symmetric d = 4 General Relativity. Their recent identification as special cases of ‘Poisson–sigma–models’ with simple general solution in an arbitrary gauge, allows a comprehensive discussion of the relation between the known absolutely conserved quantities in all those cases and Noether charges, resp. notions of quasilocal ‘energy–momentum’. In contrast to Noether like quantities, quasilocal energy definitions require some sort of ‘asymptotics’ to allow an interpretation as a (gauge–independent) observable. Dilaton gravitation, although a little different in detail, shares this property with the other cases. We also present a simple generalization of the absolute conservation law for the case of interactions with matter of any type.