Aedes aegypti is the predominant vector for arboviruses including dengue, Zika, and chikungunya viruses, which infect over 100 million people annually. Mosquito population replacement in which arbovirus-susceptible mosquitoes in the field are replaced by laboratory-engineered refractory mosquitoes represents a novel genetic control measure to interrupt arboviral disease cycles. For this approach, the engineered mosquitoes need to harbor two genetic components: an antiviral effector construct which is linked to a gene drive (GD). We tested the performance of two single-locus CRISPR/Cas9 based GD for Ae. aegypti population replacement in small cage populations for up to 16 generations. Starting from a low release threshold of 1:9 GD bearing males to wild-type males, we observed two GD constructs in which Cas9 was expressed from two different germline promoters, nanos and zpg, to increase in frequency in all cage populations. By G16, an average of 72% and 82% of individuals from the zpg-GD and nanos-GD populations, respectively, harbored at least one GD copy with corresponding increases in allele frequencies. This indicated that the two single-locus, CRISPR/Cas9-based homing GD exhibited continuous super-Mendelian inheritance in populations of Ae. aegypti. Gene drive blocking indel (GDBI, a.k.a. "resistant alleles") frequency was measured for each discrete generation in pooled samples from the six populations harboring GD. We found that populations with Cas9 expression under control of the nanos-promoter accumulated GDBI at more than twice the rate of those populations harboring the zpg-promoter driven GD. Based on preexisting data sets for homing and GDBI frequencies in addition to the cage trial observations, the relative contributions of sex-specific homing rates, maternal Cas9 deposition and potential fitness effects were modeled in MGDrivE for both GD, further explaining their divergent performance. Our study demonstrates the feasibility of low-threshold, single-locus CRISPR/Cas9 based GD for Ae. aegypti population replacement.