This is the abstract of the paper "Abstract Degenerate Cauchy Problems in Locally Convex Spaces" by Jin Liang and Ti-Jun Xiao. For the whole paper send the command get evolve-l 99-00048 to: "listserv@rz.uni-karlsruhe.de". Instead you may get the paper at "http://ma1serv.mathematik.uni-karlsruhe.de/evolve-l/index.html" too. Abstract: This paper is concerned with the abstract degenerate Cauchy problem $(DCP)$: $\dfrac{d}{dt}Bu(t)=Au(t)$ $(t\geq 0),$ $Bu(0)=Bu_0,$ where $A$ and $B$ are closed linear operators in a sequentially complete locally convex space. A $C$-propagation family for $(DCP)$ is introduced, leading to a general $C$-wellposedness result about ($DCP)$. Moreover, conditions are given ensuring the existence of $C$-propagation families for those ($DCP)$ with differentia operators, on various function spaces with Fr\'{e}chet topologies, as coefficient operators. These results are new even in the case of Banach spaces.