The article deals with the problem of proving in a special pre-trial investigation, namely, when investigating judge examines an application for a special pre-trial investigation, and in the context of the defence party as the subject of proving. Two types of local subject of proving were distinguished in the case of consideration by the investigating judge of an application for a special pre-trial investigation: the general (based on the Chapter 241 of the CPC of Ukraine) and a special local subject of proving (based on section 201 of Section XI «Transitional Provisions» of the CPC of Ukraine) containing elements of grounds and conditions for conducting a special pre-trial investigation, as well as compliance with the content of an application for conducting a special pre-trial investigation to the requirements of the CPC of Ukraine. It was substantiated that in order to create a legal basis for giving testimonies (explanations) by a suspect during a special pre-trial investigation, affidavit should be introduced in the CPC and used, which will act as an additional (in relation to the videoconference) guarantee of the realization of the procedural right of the suspect — the right to give testimonies, an explanation that is necessary for realization of the right to a fair trial.