The work considers the motion of a spherical pendulum taking into account weak conservative nonlinearity and under the influence of external or internal friction forces. For both friction options, a dissipative function is constructed and equations of motion are derived containing the system’s own cubic nonlinearity, which are written in a complex form convenient for further actions. Based on the averaging method, an approximate solution is constructed for a system under the action of one or another type of friction, and one can obtain expressions for simpler models from it. The results found are clearly illustrated in the form of trajectories of a spherical pendulum, which correspond to various models, in projection onto the horizontal plane. The solutions obtained make a certain contribution to the theory of motion of a spherical pendulum and can be useful for a variety of practical applications in the field of the nonlinear oscillations and the dynamics of dissipative systems.