We present a nonparametric methodology for evaluation of agreement between multiple methods of measurement of a continuous variable. Our approach is unified in that it can deal with any scalar measure of agreement currently available in the literature, and can incorporate repeated and unreplicated measurements, and balanced as well as unbalanced designs. Our key idea is to treat an agreement measure as a functional of the joint cumulative distribution function of the measurements from multiple methods. This measure is estimated nonparametrically by plugging-in a weighted empirical counterpart of the joint distribution function. The resulting estimator is shown to be asymptotically normal under some specified assumptions. A closed-form expression is provided for the asymptotic standard error of the estimator. This asymptotic normality is used to derive a large-sample distribution-free methodology for simultaneously comparing the multiple measurement methods. The small-sample performance of this methodology is investigated via simulation. The asymptotic efficiency of the proposed nonparametric estimator relative to the normality-based maximum likelihood estimator is also examined. The methodology is illustrated by applying it to a blood pressure data set involving repeated measurements from three measurement methods.