This paper discusses the I(2) model with breaks in the deterministic component and illustrates with an analysis of German and US prices, exchange rates, and interest rates in 1975--1999. It provides new results on the likelihood ratio test of overidentifying restrictions on the cointegrating relations when they contain piecewise linear trends. One important aim of the paper is to demonstrate that a structured I(2) analysis is useful for a better understanding of the empirical regularities underlying the persistent swings in nominal exchange rates, typical in periods of floating exchange rates.