Massive Open Online Courses (MOOCs) is an advanced form of education in the modern world. With all the advantages this format has, it is difficult to leave unchanged all the procedures included into the traditional teach-learn-assess training cycle; this difficulty can be explained by the specific form of teaching. Peer assessment is usually used to overcome these objective obstacles, although unmoderated peer assessment is questioned by experts and is not trusted much by students (and thus, accordingly, entails a decreasing motivation as students withhold from assessing performance of their peers and withdraw from learning platforms). The works dedicated to this issue mainly deal with multiple ways to resolve it within the scope of the programmers' approach or the approach of the training platform moderators. Our study deals with the question of whether correctly formulated assignments and a methodologically justified sequence of assignments help to overcome these difficulties. The study was performed with the use of questionnaires for students of various academic years (2017-2019) taking part in one MOOC, and with quantitative and qualitative analysis of the performed assignments for peer assessment for 2017 (within the scope of that session, 947 answers were given to the self-assessment assignments, and 727 answers were given to the assignments for peer assessment). The result of the study was a supported recommendation to authors of the MOOC profile in humanities, wherein the essay was supposed to be the student’s expected answer: 1) there should be a clear correlation between the conditions of the assignment setting and the criteria used for assessment of the assignment for peer assessment; 2) self-assessment assignments built on the basis of the same principle as the peer assessment assignments should be included in the course.