An evaluation of the principal uncertainties in the computation of neutrino fluxes produced in cosmic ray showers in the atmosphere is presented .
The neutrino flux predictions are needed for comparison with experiment to perform neutrino oscillation studies .
The paper concentrates on the main limitations which are due to hadron production uncertainties .
It also treats primary cosmic ray flux uncertainties , which are at a lower level .
The absolute neutrino fluxes are found to have errors of around 15 % in the neutrino energy region important for contained events underground .
Large cancellations of these errors occur when ratios of fluxes are considered , in particular , the \nu _ { \mu } / \overline { \nu } _ { \mu } ratio below E _ { \nu } = 1 GeV , the ( \nu _ { \mu } + \overline { \nu } _ { \mu } ) / ( \nu _ { e } + \overline { \nu } _ { e } ) ratio below E _ { \nu } = 10 GeV and the up/down ratios above E _ { \nu } = 1 GeV are at the 1 % level .
A detailed breakdown of the origin of these errors and cancellations is presented .