In this study, external representations and the problems encountered related transformation process between representations towards limit concept were investigated. "Limit Representation Conversion Test" was administered to 41 preservice mathematics teachers studying at a state university in central Turkey during 2018-2019 academic years. In this study, which was designed with the case study model, which is one of the qualitative research models, the data were analyzed by content analysis. Unstructured interviews were made with preservice mathematics teachers whose explanations were insufficient or differed and the problems encountered were determined. It was observed that preservice mathematics teachers had most difficulties in the verbal representation type questions. It was revealed that preservice mathematics teachers who gave the wrong answers mostly had deficiencies in the concept and the process and could not fully understand the limit problems. It was determined that preservice mathematics teachers had difficulties in knowing the concept of limit point, determining the function and interpreting verbal data. It was seen that preservice mathematics teachers who proceeded towards the concept and process answered wrong due to mathematical operations errors and carelessness. When the wrong answers were examined, it was observed that errors were gathered under the themes "lack of content knowledge" and "lack of reading comprehension" for verbal type input; under the theme "carelessness" for graphical type input; under the theme "lack of content knowledge" for algebraic and numerical type input.