We describe a new representation of Hankel operators H as pseudo-differential operators A in the space of functions defined on the whole axis. The amplitudes of such operators A have a very special structure: they are products of functions of a one variable only. This representation has numerous spectral consequences both for compact Hankel operators and for operators with the continuous spectrum.2000 Mathematics Subject Classification. 47A40, 47B06, 47B25, 47B35.