We give explicit formulae for the continuous
Hochschild and cyclic homology and cohomology of biflat topological
algebras. We show that, for a continuous morphism $\varphi:{\mathcal
X}^*\rightarrow{\mathcal Y}^*$ of complexes of complete nuclear
DF-spaces, the isomorphism of cohomology groups
$H^n(\varphi):H^n({\mathcal X}^*)\rightarrow H^n({\mathcal Y}^*)$ is
automatically topological. The continuous cyclic-type homology and
cohomology are described up to topological isomorphism for the
following classes of biprojective topological algebras: the algebra of
smooth functions $\mathcal{E}(G)$ on a compact Lie group G, the algebra
of distributions $\mathcal{E}^*(G)$ on a compact Lie group G; the
tensor algebra $E\hat{\otimes} F$ generated by the duality $(E, F,
<\cdot, \cdot>)$ for nuclear Fr\'echet spaces E and F or for
nuclear DF-spaces E and F; nuclear biprojective K\"{o}the algebras
$\lambda(P)$ which are Fr\'echet spaces or DF-spaces.