Injection tests can give such information as the effective mobilities of fluids, wellbore damage, and saturation change during displacement, which often require use of rate and pressure data. Although exact solutions for injection and falloff pressure response of a well in an infinite reservoir may be obtained for a constant injection rate, they are not readily extended for the general case of varying flow rates and bounded reservoirs. We present a perturbation theory for multiphase testing that leads to a weakly nonlinear convolution and give a technique to calculate pressure response rapidly for arbitrary flow rates for this form of convolution. The technique is specifically suited for solving inverse problems with nonlinear estimation. We present modifications to the solutions for positive and negative skin factors and demonstrate that the effect of wellbore storage is not easily accounted for in an injection test, unlike single-phase well testing. We give a procedure to correct the system response to storage and propose a variable-rate injection test to improve system parameter estimation. The main idea of the test is to excite the reservoir sequentially and continuously to keep it under strong transient conditions. We present interpretation results for such a sequential testing.