This is the abstract of the paper "Approximation and Asymptotic Behaviour of Evolution Families " by Charles J.K. Batty and Ralph Chill. For the whole paper send the command get evolve-l 01-00001 to: "listserv@uni-karlsruhe.de". Instead you may get the paper at "http://ma1serv.mathematik.uni-karlsruhe.de/evolve-l/index.html" too. Abstract: Let $(A(t))_{t\ge 0}$ and $(B(t))_{t\ge 0}$ be two families of closed operators satisfying the Acquistapace-Terreni conditions or the Kato-Tanabe conditions, or assumptions of maximal regularity, and let $(U(t,s))_{t>s\ge 0}$ and $(V(t,s))_{t>s\ge 0}$ be the associated evolution families. We obtain some estimates for $\| U(t,s) -V(t,s)\|$ in terms of $\| A(\tau)^{-1} -B(\tau)^{-1}\|$ for $s \le \tau \le t$. We deduce some results showing that if $\| A(\tau)^{-1} -B(\tau)^{-1}\| \to 0$ sufficiently quickly as $\tau\to\infty$ then $U$ and $V$ have similar asymptotic behaviour. ------------------ http://www.uni-karlsruhe.de/~listserv/ -------------------