Deterministic Realtime Languages Book and Greibach (V. Book, Ronald &amp; A. Greibach, Sheila. (1970). Quasi-realtime languages. Theory of Computing Systems. 4. 97-111. 10.1007/BF01705890.) prove that non-deterministic linear time Turing machines are equivalent to quasi-real-time such machines.

The authors say: " For deterministic machines, linear time is strictly more powerful than real-time; here we show that for nondeterministic machines linear time and real-time have the same power. "
However, they do not cite or prove the claim that linear time deterministic machines are more expressive than realtime deterministic such machines.
In a 1967 pager, Al Rosenberg gave the example of a language which is deterministic linear time but not deterministic quasi-realtime that Book &amp; Greibach probably refer to. 
Rosenberg mentions that such examples were published previously by himself and Cole.