Methods and algorithms are developed for the numerical simulation of stellar scintillations in the atmosphere during satellite observations. Estimates of the accuracy of remote measurements of the ozone content in the atmosphere are obtained on the basis of the data on stellar radiation observed from space with allowance made for scintillations under different observation conditions. The dependence of the measurement accuracy on the spectral correlations of scintillations is studied. It is shown that a noticeable increase of errors in determining the ozone content is due to stellar scintillations and may reach, at least, a few percent. Such an increase is out of the limits of errors allowable nowadays in determining the gas content of the atmosphere. The methods of the numerical simulation of stellar scintillations and their consideration in determining the gas content from the results of satellite measurements of the atmospheric transparency require further development.