When unit-root tests are used to test the income convergence hypothesis for individual OECD economies, their growth paths are usually found to be systematically related to that of the benchmark economy (typically, the US). However, more mixed evidence of such a relationship has been found for Latin American economies, suggesting their growth process is different from that of the developed world. Using recently developed Fourier-type tests, we find evidence that growth in almost all Latin American economies is actually systematically related to that of the US. However, the relative income level to which some have converged is quite low.