Quasi-Newton methods are well known iterative methods for solving nonlinear problems. At each stage, a system of linear equations has to be solved. However, for large scale problems, solving the linear system of equations can be expensive and may not be justified when the iterate is far from the solution or when the matrix is an approximation to the Jacobian or Hessian matrix. Instead we consider a class of inexact quasi-Newton methods which solves the linear system only approximately. We derive conditions for local and superlinear rate of convergence in terms of a relative residual.