The first is German made by Ochsenkopf (Ox head - I think) has BBV.Wi-Nr.2493 stamped and No 23 which presumably refers to the blade length as it’s 23cm. The short handle is original and the blade doesn’t seem to have ever been sharpened.
Could it have been a shingling axe ? What’s the bit that sticks up on the top of the poll for ?
The second one is a real mystery - it has a curved blade ! Someone gave it to me at the Formby Point Bodgers Ball several years ago. It doesn’t seem all that old and has the remains of a sticker which I think says Diamond brand.
Could it be for chopping out curved shapes or cutting round corners ?