Previous expressions for the dipole moment matrix elements of the vibration-rotation bands of diatomic molecules, based on a quintic anharmonic oscillator potential, a cubic dipole moment function, and third order perturbation theory, are extended for the 1-0 and 2-0 bands to include second-order contributions. Line intensities in the 1-0 band of HCl are measured with 0.02 cm -1 resolution and analyzed to obtain a band intensity S 01 of 135 cm -2 atm -1 at 300°K and the following Herman-Wallis factor: F 01(m) = 1 - 0.0260 m + 4.5 × 10 -4m 2. Similar measurements are made in the 2-0 band of HCl with 0.04 cm -1 resolution and yield S 02 = 3.73 cm -2 atm -1 and F 02(m) = 1 - 0.0086 m + 4.1 × 10 -4m 2. These results and the previous 3-0 band intensity data are incorporated with the dipole moment matrix elements above to obtain the following dipole moment function for HCl: M( r) = 1.095 + 0.905( r - re) - 0.066( r - re) 2 - 0.73( r - re) 3, where r - re is in angstroms and M( r) is in Debyes. The half-widths of self-broadened lines of HCl in the 2-0 band are measured directly. The results are somewhat lower than previous measurements for | m| < 8. Previous results for the dipole moment function of HCl are discussed as is the importance of second-order contributions to the dipole moment matrix elements. It is pointed out that the Morse oscillator results for HCl for a quadratic dipole moment agree reasonably well with those of the anharmonic oscillator.