In this paper we extend the notion of equal convergence of Császár and Laczkovich with the help of ideals of the set of positive integers and introduce the ideas of $\Cal{I}$ and $\Cal{I}^*$-equal convergence and prove certain properties. Throughout the investigation two classes of ideals, one satisfying ``Chain Condition'' and another called $P$-ideals play a very important role. We also introduce certain related notions of convergence and prove an Egoroff-type theorem for $\Cal{I}^*$-equal convergence.