  The zero forcing number $Z(G)$ of a graph $G$ is the minimum cardinality of a
set $S$ with colored (black) vertices which forces the set $V(G)$ to be colored
(black) after some times. "color change rule": a white vertex is changed to a
black vertex when it is the only white neighbor of a black vertex. In this
case, we say that the black vertex forces the white vertex. We investigate here
the concept of connected zero forcing set and connected zero forcing number. We
discusses this subject for special graphs and some products of graphs. Also we
introduce the connected propagation time. Graphs with extreme minimum connected
propagation times and maximum propagation times $|G|-1$ and $|G|-2$ are
characterized.
