In this paper to study some basic properties of fuzzy soft topological spaces, we define quasi fuzzy soft compactness. We also introduced some basic definitions of compact space and theorems of the concept. Keyword-Fuzzy soft topology, soft set, fuzzy soft compactness, weakly and Strong fuzzy compact spaces. I.INTRODUCTION In many complicated problems arising in the fields of engineering, social science, Economics, Environment, medical science etc. have various uncertainties. Fuzzy soft sets are very useful structures arising in many problems encountered in real life. The theory soft sets was initiated by Molodtsov[4 ] in 1999 for modeling uncertainty present in real life. Roughly speaking a soft set is a parameterized classification of the objects of the universe P.K.Maji , R. Biswas ,A.R.Roy[ 8] also initiated in more generalized concept of fuzzy soft sets which is a combination of fuzzy set and soft set . In recent times, researchers have contributed a lot towards fuzzification of soft set. Neog, Sut ,Hazarika[10 ] introduced fuzzy soft topological spaces . Some others ([5], [6], [7] , [9]) studied on the compact fuzzy soft topological spaces. My main aim in this paper is to develop the basic properties of quasi fuzzy soft compact spaces and establish several equivalent forms of fuzzy soft compactness which are useful applications.