For real-Time sparse systems identification applications, Proportionate-Type Least Mean Square (Pt-LMS) algorithms are often preferred to their normalized counterparts (Pt- NLMS) due to lower computational complexity of the former algorithms. In this paper, we present the convergence analysis of Pt-LMS algorithms. Without any assumptions on input, both first and second order convergence analysis are carried out and new convergence bounds are obtained. In particular, it establishes the universality of the steady-state mean square deviation. Detailed simulation results are presented to validate the analytical results.