In rational homotopy theory there are two concepts,formal and coformal spaces.I want to know example of a space which is
1)not formal and coformal,
2)rationally hyperbolic and not coformal.



Rational formal and coformal space
In this paper you will find examples that fits with your first question:
<http://www.sciencedirect.com/science/article/pii/S0040938303000053>
"Elliptic rational spaces whose cohomologies and homotopies are isomorphic"
Tetsu Nishimotoa, Hiroo Shiga, Toshihiro Yamaguchi.


The authors consider a family of elliptic spaces that are not formal nor coformal.
These examples are very interesting, they build two simply-connected closed smooth manifolds $M\_1$, $M\_2$ such that


1. they have isomorphic rational cohomology algebra,
2. they have isomorphic rational homotopy Lie algebras $\pi\_\*(\Omega M\_i)\otimes \mathbb{Q}$,
3. they are not rationally homotopy equivalent.


