The main problem with investment in capital market is the choice of stocks, that is which share of individual stock should be part of portfolio composition. In 1959, Harry Markowitz first formulates this problem mathematically. In following years due to certain limitations of the Markowitz's model, alternative models of portfolio optimization started to develop. Considering some advantages of alternative models of portfolio optimization compared to the original Markowitz model, it is very useful to consider possibility of applying alternative models to the Croatian capital market, which is actually the purpose of this thesis. Selected alternative models considered are portfolio optimization model with absolute deviation, minimax portfolio optimization model and portfolio optimization model with lower semi-variance. Monthly yields of ten stocks, which were continuously included in the CROBEX index throughout the observed period from January 2015 to January 2020, were used as data for formation of efficient model portfolios. First, Markowitz's model was applied to the Croatian capital market. Fifteen efficient portfolios were formed according to the Markowitz model, and the results of the model were graphically presented and interpreted. After the Markowitz's model, alternative models were applied. All selected alternative models have been applied to the Croatian capital market. Fifteen efficient portfolios were formed for each alternative model, and results of alternative models were graphically presented and interpreted. A comparison of results between selected models was also made. First, differences among portfolio compositions of selected models were discussed. It turned out that the greatest differences in portfolio composition occur between the minimax model and the Markowitz's model, while portfolios generated by the optimization model with absolute deviation and the Markowitz model are the most similar. Another way to compare the optimization results of the selected models was to select a “common” risk measure. The standard deviation, that is the risk measure in Markowitz's model, was chosen as a "common" risk measure, and standard deviation was calculated for all portfolios of alternative models. It has been shown that at lower levels of portfolio return the Markowitz's model is better than alternative models because it generates less portfolio risk in terms of standard deviation. But at higher levels of portfolio returns there is not much difference between the Markowitz's model and alternative models when compared by using the criterion of portfolio return and standard deviation as a measure of risk.