Eddy-current methods are the nondestructive methods of choice for the measurement of tube properties: inner radius, wall thickness and electromagnetic properties (relative magnetic permeability and electrical conductivity). Eddy-current systems, that measure tube properties from the interior of tube in situations where the exterior is not accessible (e.g. oil-well), employ multiple excitation frequencies and several coil pairs. Reduction in number of coils and frequencies can improve the robustness and reliability of such systems. In this thesis, analytical models have been derived of the magnetic field distribution and impedance of a coil placed axially inside a metal tube. A novel procedure has been proposed for correction of electromagnetic thickness measurement for changes in tube electromagnetic properties. Permeability measurement has been shown to be applicable to tube grade identification and stress evaluation. Furthermore, the single-coil method has been presented for simultaneous determination of tube inner radius and permeability-to-conductivity ratio. This is achieved through minimization of difference between the model prediction and the actually measured impedance of a single coil at a single frequency. The single-coil method reduces total number of coils and excitation frequencies required for measurement of tube properties. In order to confirm practical realizability of the method, sensitivity and error analyses have been made with respect to tube properties and coil dimensions. Due attention has been paid to other influential factors not included in the model, such as temperature, material non-idealities, coil decentralization, etc. The experimental results, obtained for several tubes, validate the proposed procedure within the range of 10 kHz to 100 kHz for both nonmagnetic and ferromagnetic tube materials. Further improvements of the method have been proposed. Requirements for the single-coil system have been established relating to operation in a high-temperature environment, ranges of tube properties to which the system is applicable, and accuracy of inner radius measurement. An electronic instrumentation design, based on a digital signal processing approach, has been presented.