  We present the observation of Cyg X-1 in hard spectral state performed during
the AGILE Science Verification Phase and Observing Cycle 1 in hard X-rays (with
SuperAGILE) and gamma rays (with the GRID) and lasting for about 160 days with
a live time of $\sim 6$ Ms.
  We investigate the variability of Cyg X-1 in hard X-rays at different
timescales, from $\sim 300$ s up to one day, and we apply different tools of
timing analysis, such as the autocorrelation function, the first order
structure function and the Lomb-Scargle periodogram, to our data (from
SuperAGILE) and to the simultaneous data in soft X-rays (from RXTE/ASM). We
conclude our investigation with a search for emission in the energy range above
100 MeV with the maximum likelihood technique. In the hard X-ray band the flux
of Cyg X-1 shows its typical erratic fluctuations at all timescales with
variations of about a factor of two that do not affect significantly the shape
of the energy spectrum. From the first order structure function we find that
the X-ray emission of Cyg X-1 is characterized by \textit{antipersistence},
indication of a negative feedback mechanism at work. In the gamma ray data a
statistically significant point-like source at the position of Cyg X-1 is not
found and the upper limit on the flux is $\mathrm{5 \times 10^{-8} \; ph \;
cm^{-2} \; s^{-1}}$, over the whole observation (160 days).
  Finally we compare our upper limit in gamma rays with the expectation of
various models of the Cyg X-1 emission, of both hadronic and leptonic origin,
in the GeV -- TeV band. The time history of Cyg X-1 in the hard X-ray band over
13 months (not continuous) is shown. Different tools of analysis do not provide
fully converging results of the characteristic timescales in the system,
suggesting that the timescales found in the structure function are not
intrinsic to the physics of the source.
