The basic evolution stages of the product and services quality concept are briefly discussed starting with the Taylor’s system concept total quality management TQM (Total Quality Management). Given the universal nature of the ISO-9000standardseries, they were applied in the field of software engineering. The ways of the quality improvement of the software development process (DP software) are considered on the basis of maturity models. The two main maturity models are: CMMI (Capability Maturity Model Integration) and SPICE (Software Process Improvement and Capability dEtermination). CMMI is implemented in two versions - discrete and continuous. The first one corresponds to the concept of "maturity level," and the second - to the "opportunity level". The assessment of the current state of the DP software organization and individual focus areas relate respectively to these concepts. In contract to the CMMI model, the SPICE maturity model is implemented in only one version - continuous presentation. This model defines only the concept of "opportunity level" of individual processes. The equivalent of the focus area of the CMMI model is the concept of the SPICE model process which consists of certain operations. The main disadvantage of the CMMI model is that it does not specify a software developer’s organization. On the other hand, when using the SPICE model in relation to an individual process, experts may use the following information: project management methodology; model of the life cycle of DP software; features of the subject area; organization goals. On the basis of the considered structure and the comparative analysis of these models, their individual properties were identified, which made it possible to define the ways of DP software maturity improvement. The main of these are: the formalization of maturity models; the development of mathematical models for increasing the level of maturity of both individual processes and the whole DP software; creating a discrete maturity model based on SPICE; using the methodology of collective expert assessment of the initial state of individual focus areas of the SMMI model and the processes of the SPICE model.