Linearly Ordered Theories which are Nearly Countably Categorical

The notions of almost $\omega$-categoricity and 1-local $\omega$-categoricity are studied. In particular, necessary and sufficient conditions for their equivalence under additional assumptions are found. It is proved that 1-local $\omega$-categorical theories on dense linear orders are Ehrenfeucht and that Ehrenfeucht quite o-minimal binary theories are almost $\omega$-categorical.