The quick change of direction (i.e., agility) is an important athletic ability in numerous sports. Because of the diverse and therefore hardly predictable manifestations of agility in sports, studies noted that the improvement in speed, power, and balance should result in an improvement of agility. However, there is evident lack of data regarding the influence of potential predictors on different agility manifestations. The aim of this study was to determine the gender-specific influence of speed, power, and balance on different agility tests. A total of 32 college-aged male athletes and 31 college-aged female athletes (age 20.02 ± 1.89 years) participated in this study. The subjects were mostly involved in team sports (soccer, team handball, basketball, and volleyball; 80% of men, and 75% of women), martial arts, gymnastics, and dance. Anthropometric variables consisted of body height, body weight, and the body mass index. Five agility tests were used: a t-test (T-TEST), zig-zag test, 20-yard shuttle test, agility test with a 180-degree turn, and forward-backward running agility test (FWDBWD). Other tests included 1 jumping ability power test (squat jump, SQJ), 2 balance tests to determine the overall stability index and an overall limit of stability score (both measured by Biodex Balance System), and 2 running speed tests using a straight sprint for 10 and 20 m (S10 and S20, respectively). A reliability analysis showed that all the agility tests were reliable. Multiple regression and correlation analysis found speed and power (among women), and balance (among men), as most significant predictors of agility. The highest Pearson's correlation in both genders is found between the results of the FWDBWD and S10M tests (0.77 and 0.81 for men and women, respectively; p < 0.05). Power, measured using the SQJ, is significantly (p < 0.05) related to FWDBWD and T-TEST results but only for women (-0.44; -0.41). The balance measures were significantly related to the agility performance for men but not for women. In addition to demonstrating a known relationship between speed and agility in both genders, and a small but statistically significant relationship between power and agility in women, these results indicate that balance should be considered as a potential predictor of agility in trained adult men.