first picture seems to be Aphanizomenon spp. and the second one looks like a hormogonium of some planctonic cyanobacterium, maybe Aphanizomenon too. Did you find any colony of these filaments?
as Bohuslav suggested, it might be Aphanizomenon, but I see no aerotopes. If it is not a planktic sample, it might be benthic Anabaena (both images). It is impossible to identify it properly without better photographic documentation, because heterocytes are not always present.
The small inserted picture in second image may be Komvophoron.
I aggree, i was thinking for the first one also Aphanizomenon (those that Komarek put in the new Genre: Chrysosporum ...
And the second one aff Komvophoron schmidlei if it it was an oscillatorial, but perhaps they were filaments without acinetes and heterocistes who knows?
In the second picture you insert another picture. I think that this material could belong to the genus Borzia, Borziaceae, Oscilatoriales (see these links).
I think these all images are different stages of genus Anabaena, but it can be confirmed by details cultural study. If you need my help for identification, send me dried samples/ living culture.
thanks for you help, They are samples for defined the ecological status for the water framework directive. It is imposible to try doing cultures for each confirmation.
But i would have you in mind if in the future i would need some help.
About your first image: if there are gas vesicles (destroyed by lugol preservation) and the material is really planktonic, you can have some possibilities - Aphanizomenon, Dolychospermum, Chrysosporum or Sphaerospermopsis. Thus, is very important to be sure about the trichome structure - if the trichome is metameric or submetameric. Please, see the book of Komárek 2014 about heterocitous cyanobacteria.
The second image seems to be hormogonium or genera like Borzia or Konvophoron. You need to see the population as a whole and not isolated trichome.
Please, pay attention on the heterocites distribution: your material seems to have a metameric distribution like in Dolichospermum and not submetameric distribution like in Aphanizomenon.