Abstract: 
We prove that if $G$ is a locally compact Hausdorff group then every proper $G$-ANR space has the
$G$-homotopy type of a $G$-CW complex. This is applied to extend the James-Segal $G$-homotopy
equivalence theorem to the case of arbitrary locally compact proper group actions.

1. Departamento de Matemáticas
   Facultad de Ciencias
   Universidad Nacional Autónoma de México
   04510 México Distrito Federal, México
   
2. Department of Mathematics and Statistics
   P.O. Box 68 (Gustaf Hällströmin katu 2b)
   FI-00014 University of Helsinki, Finland