This paper considers the problem of determining the number of nonparametric factors in a multivariate nonparametric relationship. The definition given is broad enough to encompass a number of potential applications in econometrics including inferring the rank of demand, testing whether for a given set of instruments it is possible to identify a linear model, and testing arbitrage pricing theory. The paper gives methods for testing hypotheses concerning the number of factors, using series and kernel based nonparametric methods and also considers the problem of estimating the number of factors. The methods are compared in a small simulation study and an application to determining the rank of demand systems is considered.