An atomistic study of tilt grain boundary structures in f.c.c. metals has been made. The principal aim of this study is to understand the structure of long-period (`general') tilt boundaries. Boundaries for which $\Sigma \leq $ 491 were considered, where $\Sigma $ is the reciprocal density of coincidence sites. The work is presented in three parts. In this paper three series of atomistic studies of symmetrical tilt boundaries in aluminium and copper are reported. One of the main objectives is to determine whether the stress fields of localized grain boundary dislocations exist in boundaries deviated far from any short-period boundary orientations. On the basis of the results of these studies, a new structural classification of grain boundaries is introduced. Certain boundaries are found to be the fundamental structural elements of other boundaries nearby in the misorientation range. Boundaries that consist of contiguous sequences of one type of fundamental structural elements are called favoured; all other boundaries are called non-favoured. It is found that favoured boundaries are not always associated with the lowest possible values of $\Sigma $ and that the same boundaries are not necessarily favoured in all metals with the same crystal structure. With use of the pair interactions to calculate the atomic level stress tensor, the hydrostatic stress fields of the boundaries are displayed. In all cases considered the stress fields of distinct, localized intrinsic grain boundary dislocations were found in non-favoured boundaries. The concept of continuity of boundary structure with misorientation is introduced. It is shown that continuity of boundary structure requires unique boundary structures at all misorientations. With use of this concept it is demonstrated how one can predict the atomic structure and stress field of any non-favoured boundary between two known, successive favoured boundaries. It is also found that an isolated discontinuous change in boundary structure between two successive favoured boundaries may exist, depending on their translation states. Some earlier atomistic studies of tilt boundaries in f.c.c. and b.c.c. metals are reinterpreted in the light of this work.