An adaptive compensation strategy for quasi-static error correction in intrinsic machines is proposed and tested. The proposed methodology consists of systematic modelling of the machine forward kinematics, including quasi-static errors, as well as direct modelling of the inverse kinematics using nonlinear regression analysis. The result is a model which is a hybrid of physical modelling and regression analysis modelling. In addition, the methodology includes a compensation strategy of the machine contouring errors using the state observer technique for on-line adaptive compensation. A CMM is chosen as a test bed for validation of the proposed methodology. Systematic modelling is carried out in two stages for the forward and inverse kinematics. Regression based models are verified using two different tests. The statistical analysis of variance technique (ANOVA) is used to select the best model in addition to model testing using an independent set equal to approximately 10% of the fitting data. The obtained models are then employed in two compensation strategies; one for the measurement error correction, and another one for the contouring error correction by motion command modification in the forward control path. For contouring tests, the CMM behavior at different thermal states is estimated using experimentally obtained Effective Coefficient of Thermal Expansion (ECTE). Simulations of the machine in contouring selected trajectories are carried out over a range of thermal states. Results obtained show an improvement in the CMM performance to a level close to the machine resolution. The CMM performance is tested using the standard ASME B.89.1.12M-1990 evaluation test, as well as a novel modified version of the test accounting for a thermally varying environment. Machine errors are significantly reduced using the proposed methodology.