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This paper considers issues related to multiple structural changes, occurring at unknown dates, in the linear regression model estimated by least squares. The main aspects are the properties of the estimators, including the estimates of the break dates, and the construction of tests that allow inference to be made about the presence of structural change and the number of breaks. We consider the general case of a partial structural change model where not all parameters are subject to shifts. We study both fixed and shrinking magnitudes of shifts and obtain the rates of convergence for the estimated break fractions. We also propose a procedure that allows one to test the null hypothesis of, say, l changes, versus the alternative hypothesis of l + 1 changes. This is particularly useful in that it allows a specific to general modeling strategy to consistently determine the appropriate number of changes present. An estimation …