The guys correspond intellectually (8)
I believe the answer is:
mentally
'intellectually' is the definition.
(I've seen this before)
'the guys correspond' is the wordplay.
'the guys' becomes 'men' (guy can mean a man).
'correspond' becomes 'tally' (synonyms).
'men'+'tally'='MENTALLY'
(Other definitions for mentally that I've seen before include "Using the mind" , "in their heads" , "by way of intellect" , "in the head" , "Intellectually" .)