The effect of perfusion on relaxation time in tissue has only been considered for first-pass kinetics of NMR-signal after application of contrast agents. The importance of perfusion on relaxation has not yet been studied for steady state conditions, i.e., when the intravascular relaxation rate is constant in time. The aim of this study is to develop a model in which T1 relaxation is derived as a function of perfusion and intracapillary volume fraction (regional blood volume). Tissue is considered to be two-compartment system, which consists of intracapillary and extravascular space. Intracapillary relaxation differs from relaxation in the arterial system due to diffusion-exchange of magnetization from extravascular to intracapillary space. Perfusion tends to attenuate this difference and thus counteracts the effect on intracapillary relaxation. Relaxation in the extravascular and intracapillary magnetization are linked by diffusion. This dependence is presented in analytical form and a generic equation is derived. AT1 experiment is considered in which all spins of tissue and blood are inverted at the beginning. Calculations are performed for the fast exchange model of tissue. Perfusion increases relaxation enhancement of intravascular contrast agents. This effect is considerable in highly perfused tissue like myocardium. The dependence of relaxation on perfusion implies an overestimation of the regional blood volume when the calculation of the latter is based on tissue models that neglect perfusion. The model presented here is applied to predict the effect of perfusion on T1 imaging with FLASH-pulse sequences because this technique has been proven to be a powerful method to obtain T1 maps within a short time interval. For the fast exchange model, two algorithms are suggested that determine perfusion and regional blood volume from T1 imaging in the presence and absence of intravascular contrast agents.