  A group $G$ is said to be a {\it CSA}-group if all maximal abelian subgroups
of $G$ are malnormal. The class of CSA groups is of interest because it
contains torsion-free hyperbolic groups, groups acting freely on
$\Lambda$-trees and groups with the same existential theory as free groups. CSA
groups are also very closely related to the study of residually free groups and
tensor completions. In this paper we investigate which free constructions
(amalgamated products and HNN extensions) over CSA groups are again CSA. The
results are applied, in particular, to show that a torsion-free one-relator
group is CSA if and only if it does not contain nonabelian metabelin
Baumslag-Solitar groups and the direct product of the free group of rank 2 and
the infinite cyclic group.
