  This paper is concerned with the extent to which the Skolem-Bang theorems in
Diophantine approximations generalise from the standard setting of $<R,Z>$ to
structures of the form $<F,I>$, where $F$ is an ordered field and $I$ is an
integer part of $F$. We show that some of these theorems are hold
unconditionally in general case (ordered fields with an integer part). The
remainder results are based on Dirichlet's and Kronecker's theorems. Finally we
extend Dirichlet's theorem to ordered fields with $IE_1$ integer part.
