Reverberation in speech is one of the primary factors caused by delayed image of speech signal plus the intended speech signals. Reverberation degrades the quality of the speech signal when recorded by a distant microphone and in the hands free telephonic scenarios. This causes a big problem for carrying out communication between people or in automatic voice recognition applications in which the voice is not properly recognized by the voice recognition applications. Here dereverberation is performed considering two mostly used real time scenarios. They are Non blind dereverberation and Blind dereverberation. Dereverberation in a hands free scenario using various adaptive algorithms has been a research topic for several years. This scenario is considered as a Non blind situation. For this non blind situation, here two types of recently proposed adaptive algorithms are used. They are Non Parametric Variable Step Size Normalized Least Mean Square (NP VSS NLMS) and Variable Step Size Normalized Least Mean Square (VSS NLMS) adaptive filters. The scenario in which the knowledge of clear speech signal is unknown is considered to be the blind situation. Here we introduce the Non parametric Variable Step Size NLMS (NP VSS NLMS) based step size adaptive filter in Maximum kurtosis linear prediction (LP) residual of speech to remove the reverberations from the reverberated speech signal. The performances of both blind dereverberation and non blind dereverberation are analyzed using Spectrogram plot, Reverberation Index (RI) and Speech Distortion (SD) parameters.