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 $G$.
