We consider the dependence of the dynamics in nonpolar liquids as a function of pressure close to the glass transition. We show how dynamical heterogeneities lead naturally to a dependence of the dominant relaxation time tau(alpha) on two independent parameters, i.e., on both pressure P and temperature T or on both density rho(eq) and temperature, without assuming the presence of energy barriers. The predictions of our model regarding the dependence of tau(alpha) as a function of pressure are discussed and compared to experimental data. Our model can account quantitatively for this dependence in the case of nonpolar molecular liquids such as 1,1'-di(4-methoxy5-methylphenyl)cyclohexane (BMMPC) and 1,1'-bis(p-methoxyphenyl)cyclohexane (BMPC) up to pressures a few hundred atmospheres and can account approximately for the slope [d log(tau(alpha))]/dP at zero pressure in the case of flexible polymers such as poly(methyltolylsiloxane) (PMTS) and poly(methylphenylsiloxane) (PMPS). We propose that nonpolar molecular liquids could be more systematically studied as model systems for understanding in detail glass transition mechanisms, which should be helpful for making progress on more complex systems, e.g., polymers with both polar and nonpolar interactions.