Nonlinear parametric vibrations of electrodynamical loudspeaker diaphragm having a form of a thin elastic shell of revolution close to a cone under the action of axial periodic load are considered. As experiments show parametric vibrations appear in the specific frequency regions and under the certain 'critical' value of the driving force and they are subjectively audible as coloration of the sound. The character of parametric vibrations and the influence of constructive loudspeaker parameters on it are examined. Several mathematical models based on the system of nonlinear differential equations are constructed. Using the developed asymptotic method and software the frequency domains and amplitudes of the loudspeaker diaphragm parametric vibrations are determined. Interaction of non-axisymmetric and axisymmetric vibrations as well as the interaction of transverse forms with different number of waves in circumferential direction are investigated.