Let \(F\) be a family of \(k\)-valued algebroidal functions defined in a region \(D\) on the Riemann sphere. Using promixity measured by Hausdorff distance (defined in the paper), the authors present six theorems about the normality of \(F\), one of which is that \(F\) is normal on \(D\) if and only if \(F\) is equicontinuous on \(D\).