Calculations of time-resolved fluorescence anisotropy from a pair of chromophores coupled by an excitation transfer interaction are presented. For the purpose of investigating the effects of nuclear motion on the energy transfer and anisotropy, an illustrative model is developed that provides each chromophore with a single intramolecular vibrational mode. Account is taken of noninstantaneous excitation and time- and frequency-resolved detection. Effects of excitation pulse duration, detection window duration and frequency resolution, and excitation transfer coupling strength on the time-resolved anisotropy are examined in detail. Effects of vibrational relaxation and dephasing are also examined using a simplified Redfield description of the effects of coupling to a thermal bath.