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The uncertainties that affect the prediction of solar neutrino Auxes are evaluated with the aid of standard solar models. The uncertainties are determined from available data for all measured quantities that are known to affect significantly the neutrino fluxes; these include nuclear reaction rates, the solar constant, and the primordial surface composition of the sun. Uncertainties in theoretical quantities (such as the stellar opacity, the equation of state, and the rate of the proton-proton reaction) are estimated from the range of values in published state-of-the-art calculations. The uncertainty in each neutrino flux that is caused by a specified uncertainty in any of the parameters is evaluated with the aid of a series of standard solar models that were constructed for this purpose; the results are expressed in terms of the logarithmic partial derivative of each flux with respect to each parameter. The effects on the neutrino fluxes of changing individual parameters by large amounts can usually be estimated to satisfactory accuracy by making use of the tabulated partial derivatives. An overall "effective 3o. level of uncertainty" is defined using the requirement that the true value should lie within the estimated range unless someone has made a mistake. Effective 3o. levels of uncertainty, as well as best estimates, are determined for the following possible detectors of solar neutrinos: