After Chiappe, Ji, Ji & Norell, 1999, Clarke & Norell, 2002, Chiappe, 2002b, Zhou & Zhang, 2005, and Zhou et al., 2009

<==o Ornithuromorpha Haeckel, 1866 sensu Chiappe et al., 1999 [Ornithurae Haeckel, 1866 non Chiappe, 1991 sensu Feduccia 1997, Zhou & Zhang, 2005; Euornithes sensu Sereno, 2005]
   |?- †Chaoyangia beishanensis Hou & Zhang, 1993 [Chaoyangiaformes: Chaoyangidae:]
   |--+-- †Vorona berivotrensis Forster, Chiappe, Krause, & Sampson, 1996 sensu Clarke & Norell, 2002 and Chiappe, 2002
   |  `-- †Archaeorhychus spathula
   `--+-- †Patagopteryx deferrariisi Alvarenga & Bonaparte, 1992 [Patagopterygiformes]
      `--+-- †Hongshanornis longicresta Zhou & Zhang, 2005
         `--+--+-- †Liaoningornis longiditrus Hou, 1997 [Liaoningornithiformes: Liaoningornithidae:]
            |  `--+--+-- †Yixianornis grabaui Zhou & Zhang, 2001  [Chaoyangiaformes:]
            |     |  `-- †Songlingornis linghensis Hou, 1996 sensu Zhou et al., 2009 [Chaoyangiaformes: Songlingornithidae:]
            |     `--o †Yanornis Zhou & Zhang, 2001 [Yanornithiformes: Yanornithidae:]
            |        |-- †Y. martini Zhou & Zhang, 2001
            |        `-- †Y. chaoyangensis
            `--+?- †Gargantuavis philoinos Buffetaut & Le Loeuff, 1998
               `--o Ornithurae Haeckel, 1866 sensu Clarke & Norell, 2002 [non Chiappe, 1991]
                  |-- †Apsaravis ukhaana Norell & Clarke, 2001
                  `--o Ornithurae Haeckel, 1866 sensu Padian & Chiappe 1998 [non Chiappe, 1991]
                     |?- †Neogaeornis wetzeli Lambrecht, 1929
                     |-- †Hesperornithiformes Fürbringer, 1888 [Odontornithes Marsh, 1880, Odontognathe Stejneger, 1885]
                     `--+?- †Gansus yumensis Hou & Liu, 1984 [Gansuiformes]
                        `--o Carinatae
                           |?- †Carinatae genera et species indet. [NHMM/RD 271] [“basal carinate from Belgium”]
                           |--o †Ichthyornithiformes [Ambiortimorphae sensu Feduccia, 1996]
                           |  |?- †Holbotia ponomarenkoi Kurochkin, 1982 [nomen nudum]
                           |  |?- †Apatornis celer (Marsh, 1873) [Ichthyornis celer Marsh, 1873] [Apatornithiformes]
                           |  |--o †Ambiortidae Kurochkin, 1982
                           |  |  |-- †Ambiortus dementjevi Kurochkin, 1982 [Ambiortiformes Kurochkin, 1982]
                           |  |  `-- †Otogornis genghisi Hou, 1994
                           |  `--o †Ichthyornis Marsh, 1880 [1872??] [Colonosaurus Marsh, 1872; Plegadornis Wetmore, 1962; Angelinornis Kashin, 1972] [Ichthyornithiformes]
                           |     |-- †I. sp.A [Tokaryk, Cumbaa & Storer, 1997] [Late Cretaceous, Pasquia Hills, Saskatchevan]
                           |     |-- †I. sp.B [Tokaryk, Cumbaa & Storer, 1997] [Late Cretaceous, Pasquia Hills, Saskatchevan]
                           |     |-- †I. dispar Marsh, 1880 [1872??] [I. victor]
                           |     `-- †I. antecessor Marsh, 1880 [1872??]
                           `--+-- †Limenavis patagonica Clarke & Chiappe, 2001
                              |?- †Piksi barbarulna Varricchio, 2002
                              `-- Neornithes Gadow, 1893 [Aves sensu stricto (Gauthier 1986)] (modern birds; nykylinnut)

Ornithuromorpha incertae sedis:

Hollanda luceria Bell, Chiappe, Erickson, Suzuki, Watabe, Barsbold & Tsogtbaatar, 2009 [Hollandaornis birdus, lapsus calami] L.Cret. CAs.

    †LimnornithiformesEurolimnornithidaeEurolimnornis Kessler & Jurczak, 1986 [Limnornis Kessler & Jurczak, 1984, non Limnornis Gould, 1839]

    †PalaeocursornithiformesCursornithidaePalaeocursornis Kessler & Jurczak, 1986 [nomen dubium]

Note:

Verricchio's (2002) tentative analysis places Piksi barbarulna close to galliform-tinamiforms, thus I place it as a tentative sistergroup to Neornithes. Current phylogeny and composition of Ornithuromorpha is also tentative. This is mainly caused by the fragmentary and poor quality of their fossils. One can say that many of these species are based such a fossils that they are practically nomina dubina -forms

Some defenitions:

Ornithuromorpha: All avialaens closer to Gallus than Enantiornis
Ornithurae: Least inclusive clade containing Gallus and Hesperornis.
Carinatae: Least inclusive clade containing Gallus and Ichthyornis
Aves: Least inclusive clade containing all living birds and their fossil relatives (makes Neornithes synonomous with Aves).

Reference(s):