This paper investigates some fundamental properties of 2-way alternating mu
lti-counter automata (2amca's) with only existential (universal) states whi
ch have sublinear space and 1 inkdot. It is shown that for any function s(n
) greater than or equal to log n such that log s(n) = o(log n), s(n) space-
bounded 1-inkdot 2amca's with only existential states are incomparable with
the ones with only universal states, and the ones with only existential (u
niversal) states are not closed under complementation.