Abstract: Chain-of-Thought (CoT) prompting empowers the reasoning abilities of Large Language Models (LLMs), eliciting them to solve complex reasoning tasks in a step-wise manner. However, these capabilities appear only in models with billions of parameters, which represent an entry barrier for many users who are constrained to operate on a smaller model scale, i.e., Small Language Models (SLMs). Although many companies are releasing LLMs of the same family with fewer parameters, these models tend not to preserve all the reasoning capabilities of the original models, including CoT reasoning. In this paper, we propose a method for aligning and transferring reasoning abilities between larger to smaller Language Models. By using an Instruction-tuning-CoT method, that is, an Instruction-tuning designed around CoT-Demonstrations, we enable the SLMs to generate multi-step controlled reasoned answers when they are elicited with the CoT mechanism. Hence, we instruct a smaller Language Model using outputs generated by more robust models belonging to the same family or not, evaluating the impact across different types of models. Results obtained on question-answering and mathematical reasoning benchmarks show that LMs instructed via the Instruction-tuning CoT method produced by LLMs outperform baselines within both in-domain and out-domain scenarios.