Let $(A, A_o)$ be a topological quasi *-algebra, which means in particular that $A_o$ is a topological *-algebra, dense in $A$. Let $pi^o$ be a *-representation of $A_o$ in some pre-Hilbert space ${cal D} subset {cal H}$. Then we present several ways
of extending $pi^o$, by closure, to some larger quasi *-algebra contained in $A$, either by Hilbert space operators, or by sesquilinear forms on ${cal D}$. Explicit examples are discussed, both abelian and nonabelian, including the CCR algebra.
