The paper considers global models of motion of a spherical pendulum in the presence of external or internal friction. Equations of the system motion for the angles of nutation and precession are derived, and in both cases it is possible to exclude the precession angle from consideration and obtain a single equation for the nutation angle, which is reduced to a convenient dimensionless form. Using numerical integration for each dissipation variant, the dependence of the nutation angle on dimensionless time is determined, which is displayed in graphical form. For greater clarity, envelope lines are also plotted on the graphs, which are found from a previously known approximate analytical solution, and they are in very good agreement with the results of the numerical study. The conclusions drawn in the paper are of interest for analytical mechanics and dynamics of dissipative pendulum systems, and they may also be useful in engineering problems.