The MHD normal modes of oscillation of coronal magnetic structures are studied by including two aspects that have not been considered in previous theoretical works of this kind, namely the effects of the magnetic field shear and of the longitudinal propagation in the oscillatory properties of solar coronal structures. We show that, in a cold plasma, the inclusion of these two aspects produces the coupling of fast modes, characterized by a global velocity structure and a discrete spectrum of frequencies and Alfven continuum modes, characterized by a velocity perturbation confined to given magnetic surfaces, in such a way that no pure fast modes nor pure Alfven modes exist, but modes with mixed properties arise. These oscillatory modes display a global spatial distribution together with a non-square integrable singular behaviour on certain magnetic surfaces. Moreover, the mode coupling is such that, under some circumstances, the Alfvenic contribution is also in the form of a smooth velocity profile covering a range of magnetic surfaces instead of a singularity on a fixed magnetic surface. The coupling between fast and Alfven modes is governed by the parity of their eigenfunctions in the direction along the equilibrium magnetic field. The ``parity rules'' determining the features of coupled modes in terms of their spatial structure and the values of shear and longitudinal propagation are presented. The conditions for the resonant or non-resonant interaction between modes are also discussed. We have found that the frequency of coupled modes is real when only shear or longitudinal propagation are present, but is complex when both effects exist. Also, an important result is that coupled modes may not be observable since many of them leak energy away from the solar corona.