(1) Reliable measures of population abundance are essential for managing wildlife effectively. Aerial surveys provide a rapid and efficient means of surveying large mammals and many techniques have been developed to adjust for the inability to count all animals within transects. The probability of detection varies according to a range of factors which are important to consider when estimating density. Standardised survey methods developed in flat country are not readily transferable to steep terrain due to safety, access and difficulties delineating transect widths. Other methods have logistic constraints and must adhere to various other assumptions. (2) Density estimators are seldom examined using actual population size, hence their ability to correct for true bias is unknown. Studies that compare techniques are difficult to interpret because of the uncertainty of adherence to their respective assumptions. Factors influencing detection probability, estimators that correct for bias, the validity of their assumptions and how these relate to true density are important considerations for selecting suitable methods. The aim of this study was to obtain accurate and reliable methods for estimating the density of feral goats by improving predictions of detection probability, investigating the assumptions of aerial surveys, and examining the accuracy of 15 density estimators by comparing with total counts of feral goats. (3) Group size, vegetation and observer were the most important factors influencing the probability of observing a group of goats during aerial surveys. However, different approaches to analysing these data influenced the significance of variables and the predicted probabilities. Goat colour, type of helicopter, site and rear observer experience in hours were also found to be significant (P<0.05) when using likelihood equations based on all animals in the population rather than only those in the sample. The slope of the terrain was also shown to significantly (P=0.014) affect the probability of detection. (4) Indices are commonly used in wildlife management for their simplicity and practicality, but their validity has been questioned because of variable probability of detection. Results of this study suggest aerial survey indices are useful in monitoring a range of medium-sized mammal species across space and time if differences in detection probability between species, group size, vegetation and observer are considered and their effects are standardised. (5) An assumption of most sampling regimes that is fundamental but rarely examined is that animals are not counted more than once. In this study the behavioural responses of feral goats to helicopters were investigated as a basis for estimating the probability that goats were recounted. No long-term consequences were evident in feral goat behaviour of responses to helicopters. However, helicopter surveys were found to alter the structure of 42% of groups observed, with 28% of groups merging with others and 14% splitting into separate groups. Therefore, group size estimated from the air should not be considered as biologically important, and when estimating density, researchers should also avoid using group sizes determined from independent ground observations to correct group sizes determined from aerial surveys. Goats were also more likely to flush further when helicopters were within 150 m, which is close to or within standard helicopter strip widths. Substantial movement occurred between transects and 21% of goats were estimated to be available for recounting in adjacent transects. (6) Different detection probabilities between groups of goats may be particularly relevant when using double-counting, where multiple observers are �capturing� and �recapturing� animals in the same instant. Many analyses test and adjust for this �unequal catchability� assumption in different ways, with the approaches of Huggins and Alho allowing prediction of unique probability values for a range of co-variates. The approach of Chao attempts to correct for skewed distributions in small samples. The Horvitz-Thompson approach provides a useful basis for estimating abundance (or density) when detection probability can be estimated and is known to vary between observations according to a range of independent variables, and also avoids errors associated with averaging group size. (7) After correcting for recounting, the Alho estimator applied to helicopter surveys was the most accurate (Bias = 0.02) and reliable of all techniques, which suggests that estimates were improved by taking into account unconditional detection probability and correcting individual observations according to their characteristics. The positive bias evident in the Chao (Bias = 0.28) and Petersen (Bias = 0.15) aerial survey estimators may have been a result of averaging detection probability across all observations. The inconsistency and inaccuracy of the ground-based area-count technique emphasises the importance of other assumptions in density estimation, such as representative sampling and availability bias. The accuracy of index-manipulation-index techniques was dependent on the indices used. Capture-recapture estimates using mustering showed slight negative bias (Bias = -0.08), which was likely a result of increased probability of re-capture (i.e. trap happy). Ground-based capture-resight estimates were labour intensive and positively biased (Bias = 0.13), likely due to underestimating the area sampled, or overestimating the number of unmarked individuals with each sample. (8) Helicopter survey using double-counting is recommended for estimating the density of feral goats in steep terrain. However, consideration of recounting under intensive sampling regimes and adjustments for the factors that influence unconditional detection probability is required.