This paper is concerned with the relationship between ordinary linear quasi-differential expressions, defined in terms of locally Lebesgue integrable coefficients given on an interval of the real line, and the ’classical’ differential expressions with smooth (differentiable to certain prescribed orders) coefficients. The results give necessary and sufficient conditions for the general quasi-differential expression to be equivalent to a classical expression. In an appropriate sense the results can be considered as best possible. Examples of the results are given for second-order and third-order differential expressions.