arXiv:1302.6719v1 ; Luminosity functions are one of the most important observational clues when studying galaxy evolution over cosmic time. In this paper we present the X-ray luminosity functions for X-ray detected AGN in the SXDS and GWS fields. The limiting fluxes of our samples are 9.0 ×10-15 and 4.8 ×10-16 erg cm-2 s-1 in the 0.5-7.0 keV band in the two fields, respectively. We carried out analysis in three X-ray bands and in two redshift intervals up to z ≤ 1.4. Moreover, we derive the luminosity functions for different optical morphologies and X-ray types. We confirm strong luminosity evolution in all three bands, finding the most luminous objects at higher redshift. However, no signs of density evolution are found in any tested X-ray band. We obtain similar results for compact and early-type objects. Finally, we observe the >Steffen effect>, where X-ray type-1 sources are more numerous at higher luminosities in comparison with type-2 sources. ; This research has been supported by the Spanish Ministry of Economy and Competitiveness (MINECO) under the grant AYA2011-29517-C03-01. MP, IM, and JM acknowledge Junta de Andalucía and MINECO through projects PO8-TIC-03531 and AYA2010-15169. We acknowledge support from the Faculty of the European Space Astronomy Centre (ESAC). JIGS acknowledge financial support from the MINECO under project AYA2008-06311-C02-02 and AYA2011-29517-C03-02. JG acknowledges support from the MINECO through AYA2009-10368 project. The CEFCA is funded by the Fondo de Inversiones de Teruel, supported by both the Government of Spain (50%) and the regional Government of Aragón (50%). This work has been partially funded by the Spanish Ministerio de Ciencia e Innovación through the PNAYA, under grants AYA2006-14056 and th-rough the ICTS 2009-14. ; Peer Reviewed