We make some observations concerning alternating Turing machines operating in small space. For example, we show that alternating Turing machines using o(log n) space are more powerful than nondeterministic Turing machines using the same space-bound. In fact, we show that there is a language over a unary alphabet that can be accepted by an on-line alternating Turing machine in log n space, but not by any off-line nondeterministic Turing machine in o(log n) space. We also investigate the weak vs. strong space bounds and on-line vs. off-line machines at these low tape bounds. © 1987.