Raman microspectroscopy is gaining popularity for the analysis of time-dependent biological processes such as drug uptake and cellular response. It is a label-free technique which acquires signals from a large variety of components, including cell biomolecules and exogenous compounds such as drugs and nanoparticles, and is commonly employed for in vitro analysis of cells and cell populations with no labelling or staining required. By monitoring the changes to the Raman spectra of the cell as a result of a perturbing agent (e.g. inoculation of a drug or toxic agent), one can study the associated changes in cell biochemistry involved in both, the disruption and the subsequent cellular response. The main challenge is that the Raman spectra should be data mined in order to extract the information corresponding to the different actors involved on the process. Here, we study the application of multivariate curve resolution-alternating least squares (MCR-ALS) for extracting kinetic and biochemical information of time-dependent cellular processes. The technique allows the elucidation of the concentration profiles as well as the pure spectra of the components involved. Initially, we used Ordinary Differential Equations (ODE) to simulate drug uptake and 2 responses, which were employed to simulate perturbations to experimental control spectra, creating a dataset containing 36 simulated Raman spectra. Four different scenarios governing the drug exposure-response were evaluated: an undetectable disruption (e.g. radiation), a detectable disruption (e.g. a drug) and disruption with a signal significantly larger than the biological changes induced (e.g. a resonant drug), as well as simultaneous and asynchronous responses. Subsequently, data acquired from the exposure of a pulmonary adenocarcinoma cell line (A549) to Doxorubicin was analysed. The results indicate that MCR-ALS can independently identify and isolate both the spectra of the drug and the cell 2 responses under the different scenarios. The predicted concentrations map out the drug uptake and cellular response curves. The technique shows great potential to investigate non-linear kinetics and modes of action. Advantages and limitations of the technique are discussed, providing guidelines for future analysis strategies.