TIMP is an R package for modeling multiway spectroscopic measurements. The package allows for the simultaneous analysis of datasets collected under different experimental conditions in terms of a wide variety of parametric models. Models arising in spectroscopy data analysis often have some parameters that are intrinstically nonlinear, and some parameters that are conditionally linear on estimates of the nonlinear parameters. TIMP fits such separable nonlinear models using partitioned variable projection, a variant of the variable projection algorithm that is described here for the first time. The of the partitioned variable projection algorithm allows fitting many models for spectroscopy datasets using much less memory as compared to under the standard variable projection algorithm that is implemented in nonlinear optimization routines (e.g., the plinear option of the R function nls), as is shown here. An overview of modeling with TIMP is also given that includes several case studies in the application of the package.