Apparatus for the dehumidification of an air flow, preferably a compressed air flow, comprising: - an outer box provided with first means for the damp air inlet, and with second means for the outlet of de-humidified air, - a first heat exchanger for the pre-cooling and successively heating said gas flow, and comprising two distinct and separate conduit assemblies for the reciprocal heat exchange, wherein a first conduit assembly is passed by said damp air flow coming from said first means, and a second assembly is passed by said already dried gas flow and is directed to said second means, - a second heat exchanger arranged downstream of said first heat exchanger and apt of cooling said air flow and of condensing the dampness therein contained, and comprising: a third conduit assembly passed by said gas flow to be dried and coming from said first conduits, a fourth conduit assembly thermally associated to said third assembly, and able of being supplied with a refrigerating flow and of conveying it to the relevant outlet, a collecting chamber able of intercepting and collecting the dampness condensed inside said second heat exchanger and passed by said air flow, and arranged downstream of said second heat exchanger, - a second chamber downstream of said collecting chamber, contiguous to said second heat exchanger and connected to the outside by a respective emission mouth, - a third chamber: a) not communicating to said second chamber, b) connected to the conduits of said second assembly, c) connected to the outside of said outer box by a respective inlet mouth, characterized in that the apparatus further comprises: implementing a return path from said second heat exchanger to said first heat exchanger which comprises: a first leg which at least partially crosses said collection chamber, a second leg which passes through said second chamber and which then passes through said emission mouth, a third leg branching out from said emission mouth to said inlet mouth across further de-humidifying means, a fourth leg passing through said third chamber, said first and second heat exchanger and said collection chamber being contained in a common outer box. - an outer box provided with first means for the damp air inlet, and with second means for the outlet of de-humidified air, - a first heat exchanger for the pre-cooling and successively heating said gas flow, and comprising two distinct and separate conduit assemblies for the reciprocal heat exchange, wherein a first conduit assembly is passed by said damp air flow coming from said first means, and a second assembly is passed by said already dried gas flow and is directed to said second means, - a second heat exchanger arranged downstream of said first heat exchanger and apt of cooling said air flow and of condensing the dampness therein contained, and comprising: a third conduit assembly passed by said gas flow to be dried and coming from said first conduits, a fourth conduit assembly thermally associated to said third assembly, and able of being supplied with a refrigerating flow and of conveying it to the relevant outlet, a collecting chamber able of intercepting and collecting the dampness condensed inside said second heat exchanger and passed by said air flow, and arranged downstream of said second heat exchanger, a third conduit assembly passed by said gas flow to be dried and coming from said first conduits, a fourth conduit assembly thermally associated to said third assembly, and able of being supplied with a refrigerating flow and of conveying it to the relevant outlet, a collecting chamber able of intercepting and collecting the dampness condensed inside said second heat exchanger and passed by said air flow, and arranged downstream of said second heat exchanger, - a second chamber downstream of said collecting chamber, contiguous to said second heat exchanger and connected to the outside by a respective emission mouth, - a third chamber: a) not communicating to said second chamber, b) connected to the conduits of said second assembly, c) connected to the outside of said outer box by a respective inlet mouth, characterized in that the apparatus further comprises: implementing a return path from said second heat exchanger to said first heat exchanger which comprises: a first leg which at least partially crosses said collection chamber, a second leg which passes through said second chamber and which then passes through said emission mouth, a third leg branching out from said emission mouth to said inlet mouth across further de-humidifying means, a fourth leg passing through said third chamber, a) not communicating to said second chamber, b) connected to the conduits of said second assembly, c) connected to the outside of said outer box by a respective inlet mouth, characterized in that the apparatus further comprises: implementing a return path from said second heat exchanger to said first heat exchanger which comprises: a first leg which at least partially crosses said collection chamber, a second leg which passes through said second chamber and which then passes through said emission mouth, a third leg branching out from said emission mouth to said inlet mouth across further de-humidifying means, a fourth leg passing through said third chamber, a first leg which at least partially crosses said collection chamber, a second leg which passes through said second chamber and which then passes through said emission mouth, a third leg branching out from said emission mouth to said inlet mouth across further de-humidifying means, a fourth leg passing through said third chamber,