Multinomial Processing Tree (MPT) models are a powerful and frequently used method in various research fields including cognitive psychology and social cognition. They allow for estimation and statistical tests on parameters that represent psychological processes underlying responses to cognitive tasks. So far, parameter tests in MPT models have largely relied on Null Hypothesis Significance Testing, mostly ignoring statistical power. Classical test procedures such as Neyman-Pearson tests often require very large sample sizes to reliably control Type 1 and Type 2 error probabilities. We propose Sequential Probability Ratio Tests (SPRT) as an efficient alternative. Unlike Neyman-Pearson tests, sequential tests continuously monitor the data and terminate when a predefined criterion is met. As a consequence, SPRTs typically require only about half of the Neyman-Pearson sample size without compromising error probability control. In this project, we illustrate the SPRT approach to statistical inference in single-parameter MPT models, as well as an extension based on Maximum Likelihood theory for models with more than one unknown parameter. We demonstrate the properties of the proposed test procedures by means of simulations. The R scripts for all simulations and analysis, as well as all simulated data reported in Schnuerch, Erdfelder, and Heck (2019) can be downloaded from this repository.