This paper describes current results achieved during the work on parsing of a free-word-order natural language (Czech) . It contains theoretical base for a new class of grammars - CFG extended for dependecies and non-projectivities – and also the description of the implementation of a parser and grammar-checker. The paper also describes some typical problems of parsing of free-word-order languages and their solutions (or discusssion of those problems), which are still subject of investigation. The implementation described here serves currently as a testing tool for the development of a large scale grammar of Czech. Some of the quantitative data from a processing of test sentences are also included.