We prove that if $X|_\Lambda$ has the weak specification property robustly,
where $\Lambda$ is an isolated set, then $\Lambda$ is a sectional hyperbolic
topologically mixing set and if $X|_\Lambda$ has the specification property
robustly then $\Lambda$ is a hyperbolic topologically mixing set . Also we
prove that if $X$ is a vector field that has the weak specification property
robustly on a closed manifold $M$, then the flow $X_t$ is a topologically
mixing Anosov flow and that there exists a residual subset $\SR \in
\mathfrak{X}^{1}(M)$ so that if $X \in \SR$ and $X$ has the weak specification
property, then $X_t$ is an Anosov flow.