The changes of the mode structures and attenuation constants in dielectric-coated circular metallic hollow waveguides are numerically investigated by solving the exact characteristic equations. It is shown that the mode structures in the small-core waveguides change drastically with the thickness of the coated-dielectric.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>