  We perform a dynamical system analysis of Myrzakulov or F(R, T) gravity,
which is a subclass of affinely connected metric theories, where ones uses a
specific but non-special connection, which allows for non-zero curvature and
torsion simultaneously. We consider two classes of models, we extract the
critical points, and we examine their stability properties alongside their
physical features. In the Class 1 models, which possess {\Lambda}CDM cosmology
as a limit, we find the sequence of matter and dark energy eras, and we show
that the Universe will result in a dark-energy dominated critical point for
which dark energy behaves like a cosmological constant. Concerning the
dark-energy equation-of-state parameter we find that it lies in the
quintessence or phantom regime, according to the value of the model parameter.
For the Class 2 models, we again find the dark-energy dominated, de Sitter
late-time attractor, although the scenario does not possess {\Lambda}CDM
cosmology as a limit. The cosmological behavior is richer, and the dark-energy
sector can be quintessence-like, phantom-like, or experience the phantom-divide
crossing during the evolution.
