A study examined key determinants of apprentice and trainee employment in small and medium-sized enterprises that play an increasing role in providing employment-based training in Australia. It used unit record data from four waves of the Australian Bureau of Statistics business growth and performance surveys 1994-95 to 1997-98, which sent questionnaires to 13,000 businesses nationwide that employed fewer than 200 employees. Statistical analysis, using a probit regression, was undertaken to model influence of businesses' variables on their propensity to provide apprentice and trainee training. Analysis provided no evidence of one business characteristic that triggered small and medium-sized enterprises to provide training. Larger firms, firms with a high proportion of full-time staff, and firms expanding in size within the confines of their existing sites were more likely to provide training. More stable economic conditions and the ability to expand their enterprise increased the propensity to train. Analysis supported qualitative research that found managers' educational background and traditions of apprentice training within an industry had considerable impact on the decision to take on an apprentice and provided evidence of a significant effect of a training culture on employers' propensity to provide entry-level training. (Appendixes include 26 references, method used for construction of dummy variables, and detailed results for a logistic regression.) (YLB)