These are approx AWG 20 (0.8 mm in diameter, 0.5 sq mm) and AWG 23 (0.56 mm in diameter, 0.25 sq mm), the maximum current should be 1.4A and 700mA (safe values) for copper wires.
Practically, this may be less about the wire than its
insulation temperature rating and how it is enclosed
(cooled, or not). Bare copper can stand a lot more
self-heated temperature than PVC for example, and
the conductor may be unaffected but the insulation
fail (although this may bring on the next act, Short
Circuit Follies). This is why people ask about the
application details.
but i reported maximum current for power transmission (with a bit of safety margin), that was in my thoughts the most reasonable value, based in past experience as well.
I think we are partly discussing on cross purposes, mainly because the field of application hasn't be clearly specified. Most people involved in instrument design will know which amperage is permitted by national and international standards e.g. for power supply cables or internal wiring. As an example, I quote the UL-CSA rules, which are probably a bit more restricted than other standards.