This paper This paper develops a new approach to the problem of testing the existence of a long-run level relationship between a dependent variable and a set of regressors, when it is not known with certainty whether the underlying regressors are trend- or first-difference stationary. The proposed tests are based on standard F- and t-statistics used to test the significance of the lagged levels of the variables in a first-difference regression. Two sets of asymptotic critical values are provided: one set assuming that all the regressors are I(1) and another set assuming they are all I(0). These two sets of critical values provide a band covering all possible classifications of the regressors into I(0), I(1) or mutually cointegrated. Accordingly, various bounds testing procedures are proposed. The empirical relevance of the bounds procedures is demonstrated by a re-examination of the earnings equation included in the UK Treasury macro-econometric model. This is a particularly relevant application as there is considerable doubt concerning the order of integration of variables such as the unemployment rate, union strength and the wedge between the real product wage' and the real consumption wage' that enter the earnings equation