  We discuss the Newtonian limit of boost-rotation symmetric spacetimes by
means of the Ehler's frame theory. Conditions for the existence of such a limit
are given and, in particular, we show that asymptotic flatness is an essential
requirement for the existence of such a limit. Consequently, generalized
boost-rotation symmetric spacetimes describing particles moving in uniform
fields will not possess a Newtonian limit. In the cases where the
boost-rotation symmetric spacetime is asymptotically flat and its Newtonian
limit exists, then it is non-zero only for the instant of time symmetry and its
value is given by a Poisson integral. The relation of this result with the
(Newtonian) gravitational potential suggested by the weak field approximation
is discussed. We illustrate our analysis through some examples: the two
monopoles solution, the Curzon-Chazy particle solution, the generalized
Bonnor-Swaminarayan solution, and the C metric.
