We report the synthesis and the magnetic properties of single crystalline CeRhAl4Si2 and CeIrAl4Si2 and their non magnetic La-analogs. The single crystals of these quaternary compounds were grown using Al-Si binary eutectic as flux. The anisotropic magnetic properties of the cerium compounds were explored in detail by means of magnetic susceptibility, isothermal magnetization, electrical resistivity at ambient and applied pressures up to 12.6 kbar, magnetoresistivity and heat capacity measurements. Both CeRhAl4Si2 and CeIrAl4Si2 undergo two antiferromagnetic transitions, first from the paramagnetic to an antiferromagnetic state at TN1 = 12.6 K and 15.5 K, followed by a second transition at lower temperatures TN2 = 9.4 K and 13.8 K (inferred from the peaks in the heat capacity), respectively, in conformity with an earlier report in the literature. The paramagnetic susceptibility is highly anisotropic and its temperature dependence in the magnetically ordered state suggests the c-axis to be the relatively easy axis of magnetization. Concomitantly, isothermal magnetization at 2 K along the c-axis shows a sharp spin-flop transition accompanied by a sizeable hysteresis, while it varies nearly linearly with field along the [100] direction up to the highest field 14 T of our measurement. The electrical resistivity provides evidence of the Kondo interaction in both compounds, inferred from its −lnT behavior in the paramagnetic region and the decrease of magnetic transition temperature with pressure. The heat capacity data confirm the bulk nature of the two magnetic transitions in each compound, and further support the presence of Kondo interaction by a reduced value of the entropy associated with the magnetic ordering. From the heat capacity data below 1 K, the coefficient of the linear term in the electronic heat capacity, γ, is inferred to be 195.6 and 49.4 mJ/mol K 2 in CeRhAl4Si2 and CeIrAl4Si2, respectively classifying these materials as moderate heavy fermion compounds. The main features of the magnetoresistivity measured at a particular temperature correlate nicely with the isothermal magnetization at the same temperature in these two isostructural compounds. We have also carried out an analysis of the magnetization based on the point charge crystal electric field model and derived the crystal electric field energy levels which reproduce fairly well the peak seen in the Schottky heat capacity in the paramagnetic region. Further, we have also performed electronic structure calculations using (LSDA +U) approach, which provide physical insights on the observed magnetic behaviour of these two compounds.