The characters, especially the linearity, of the response of ship oscillations among waves were investigated, and the relations between different types of expressions of linear responses, and the way to get them and to convert them each other were summarized. For example, the way to get the frequency response of the oscillation among waves from the free damping test was introduced. This is to prepare the clear understandings of the characters of responses which appear in spectra as well as in correlogram, including the cross-spectrum and the cross-covariance function, which will be treated in the analysis of oscillations among irregular waves in Part II and III of this paper.