Cyclic cohomology of certain nuclear Frechet and DF algebras

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