The interaction of parametric oscillations and self-oscillations under nonlinear parametric excitation and delay in elasticity is considered. To solve the differential equations of the system motion, the direct linearization method was used and equations for non-stationary and stationary modes of oscillations were derived. Using the Routh–Hurwitz criteria, stability conditions for stationary regimes were obtained. To find out the effect of nonlinear parametric excitation on the dynamics of mixed autoparametric oscillations, relevant calculations were carried out and a comparison was made of the results obtained in the presence and absence of delay. According to calculated data, in the presence of a delay, a change in amplitude values occurs, accompanied by a shift in the amplitude curves in the amplitude-frequency area, as well as their narrowing or broadening, compared to no lag. The presence of lag also affects the stability of oscillations.