kernel of the natural map $H_b^2(\Gamma,\mathbb{R})\to
H^2(\Gamma,\mathbb{R})$ vanishes. Together with the results of Fujiwara [@F] and Bestvina and Fujiwara [@BF] it follows easily that the image of every homomorphism of $\Gamma$ into a finitely generated word hyperbolic group or into the mapping class group of an oriented surface of finite type and negative Euler characteristic is finite [@BM02; @BF]. The latter result was earlier derived with different methods by Farb and Masur [@FM] building on the work of Kaimanovich and Masur [@KM].

The goal of this note is to present a new method for constructing nontrivial second bounded cohomology classes for a countable group $\Gamma$ from dynamical properties of suitable actions of $\Gamma$. We use it to give a common proof of extensions of the above mentioned results of Fujiwara [@F] and of Bestvina and Fujiwara [@BF] which among other things answers a question raised by Monod and Shalom [@MS; @MS05].

For the formulation of these results, call a countable group $\Gamma$ of isometries of a (not necessarily proper) hyperbolic geodesic metric space $X$ *weakly acylindrical* if for every point $x_0\in X$ and every $m>0$ there are numbers $R(x_0,m)>0,c(x_0,m)>0$ with the following property. If $x,y\in X$ are such that a 