The paper considers n-dimensional var models for variables exhibiting cointegration and common cyclical features. Two specific reduced rank vector error correction models are discussed. In one, named the “strong form” and denoted by sf, the collection of all coefficient matrices of a vecm has rank less than n, in the other, named the “weak form” and denoted by wf, the collection of all coefficient matrices except the matrix of coefficient of error correction terms has rank less than n. The paper explores the theoretical connections between these two forms, suggests asymptotic tests for each form and examines the small sample properties of these tests by monte carlo simulations.the paper proposes a sequential test procedure that is aimed at uncovering strong forms by examining weak forms. For gdp series for five latin american countries, 1950–1999, the wf appears to be supported by the data. Imposing the wf parameter restrictions leads to an improvement of forecast accuracy for these data series.