The multiexciton (MX) description of excitation energy transfer in chromophore complexes and biological light harvesting antenna systems is extended to the incorporation of exciton exciton annihilation (EEA) processes. To achieve a complete microscopic description the approach is based on intrachromophore internal conversion processes leading to nonradiative transitions from higher to lower lying exciton manifolds. Besides an inclusion of EEA the MX density matrix theory which has been utilized for a description of excitation energy transfer also accounts for a coupling to low-frequency vibrational modes and the radiation field. Concentrating on transitions from the two to the single-exciton manifold exact and approximate expressions for the EEA rate are derived. In part II of this paper the approach is applied to the LH2 antenna putting emphasis on the EEA induced change of transient absorption spectra. (C) 2003 American Institute of Physics.