Three-interval approximations ofT=f(R)andR=g(T)functions for germanium resistance thermometer (GRT)(1.4–5.7)K;(5.7–27.4)K;(27.4–100)K and platinum resistance thermometer (PRT)(14–31)K;(31–95)K;(95–325)K is carried out, using a weighted orthonormal polynomial expansion method (OPEM). A two-interval OPEM approximation ofT(R)andR(T)functions for PRT(14–70)K;(70–325)K is also presented. Our OPEM approximation of theT(R)function for the GRT and PRT, compared with other descriptions, based on Chebyshev or ordinary polynomials with the same calibration test data is discussed also. The results, shown in tables and figures, demonstrate the reliability and the advantages of the proposed OPEM, in cryogenic thermometry. ©1997 American Institute of Physics.