A robust and efficient least-squares algorithm for parameter estimation in well test analysis is presented. The algorithm parameter estimation in well test analysis is presented. The algorithm is a Levenberg-Marquardt with a "trust region" approach for global convergence along with restriction in the unknown parameters. In this approach, the selection of the step length is not parameters. In this approach, the selection of the step length is not independent on the choice of Marquardt parameter, in contrast with linear search procedure. For a homogeneous reservoir, the algorithm converges to the same result even if each initial guess differs from the final estimates in approximately three orders of magnitude. Compared with the most robust algorithm known up to now (Watson and Lee algorithm), it usually requires about half of the iterations. On the other hand, in cases involving negative skin the convergence is slowed, due to the stronger non-linear character of the problem and the bigger residuals. Introduction In the last decade, non-linear regression techniques along with constrained optimization methods have extensively been used in well test analysis. These procedures ease and enhance the parameter determination process. Iterative numerical comparisons between the observed response and the calculated response obtained from the model system with the unknown parameter values are made. The iteration ends when a numerically acceptable comparison is achieved. This method is therefore objective, more accurate and precise. Besides these advantages, it allows the analysis of complex reservoirs (multilayer, composites, finites, etc.) or of variable flow rate test, which can not be evaluated using conventional techniques. In the past, one of the difficulties in the implementation of the non-line regression algorithms in well test analysis was the evaluation of analytical expressions modeling the reservoir responses. These expressions and their derivatives were only known in the Laplace space. Rosa and Horne showed that by applying the Stehfest numerical inversion algorithm to both the analytical solutions and their derivatives, it is possible to utilize the least-squares technique to fit the experimental pressure data to any reservoir model. Particularly, they studied pressure data to any reservoir model. Particularly, they studied homogeneous, single layer and multi-layer reservoirs producing at constant flow rate. Later, this method was used by Barua and Horne for interpreting thermal recovery well test data. However, the above mentioned analysis procedure presents some practical limitations, such as the need of selecting initial values close to the best final estimates (in the leastsquares sense) in order that the algorithm converge or converge to physically acceptable values. This is mainly due to the weak global convergence of the utilized algorithm. Another difficulty, of different nature, is the convergence to unacceptable values when the study involves statistically dependent parameters. In general, this can happen when there are many parameters involved. Except in the case of a homogeneous reservoir, many reservoir models require the estimation of several parameters. Barua et al. used a modified Newton-type algorithm (Newton-Greenstadt method) in their study of ill-defined parameters. They showed that this procedure is more parameters. They showed that this procedure is more appropriate than the Gauss-type methods in cases where more than one parameter is ill-conditioned. Nevertheless, this algorithm preserves the typical non-global convergence of the second-order methods.