<p>We investigate nongeneric fold-Hopf bifurcations in a jerk system with two real parameters, specifically the transcritical-Hopf and pitchfork-Hopf bifurcations. We derive the jerk canonical form corresponding to each of these bifurcations. For the transcritical-Hopf case, we describe the parametric portrait of the associated jerk canonical form. Furthermore, using first-order averaging theory, we establish that the zero-Hopf point of this canonical form gives rise to at most one limit cycle. In addition, we discuss and compare the properties of two simple jerk systems that exhibit a pitchfork-Hopf bifurcation, especially regarding the emergence of limit cycles from the zero-Hopf point.</p>