Sorry for the shorthand. I rescued my HF-81 from my uncle's attic and needed to do a fair amount of restoration. If you are interested in a lot (too much) of information on Eico's you can check out the Yahoo Groups on Eico. The Eico has a pair of rectifier tubes (which convert AC power to DC) which are marked 6CA4/EZ81 on them. They seem to have a substantial impact on the sound quality. Many people prefer Mullard brand or Amperex brand for these tubes.
There are four identical tubes labeled 6BQ5/EL84 which are the output tubes. They are the final amplification stage tubes and they supply amplified signal to the speakers through the pair of output transformers. Some people like vintage NOS (New Old Stock) tubes in these positions, but I've been fairly happy with modern production JJ tubes or Russian equivalents in these positions. Good thing because the NOS varieties are getting expensive.
The other tubes provide amplification for the phono stage and the line stage. They are marked 12AU7 and 12AX7. The 12AX7 tubes can be replaced with modern "Mullard" label long-plate 12AX7 tubes which sound quite good.
I hope this is a bit clearer and more helpful to you. Again, this should be a nice amplifier for you long term.
Speaking of which... If yours has had nothing done to it, then you should have someone check the health of the electrolytic capacitors in the power supply. Mine were bad, and replacing them (and increasing their values somewhat) contributed a MUCH stronger bass line to my music.