An open neighbourhood of a vertex \(x\) in an undirected graph \(G\) is the set \(N(x)\) of all vertices adjacent to \(x\) in \(G\); its closed neighbourhood is \(N[x]=N(x) \cup \{x\}\). For a set \(S\) of vertices set \(N(S)=\bigcup_{x \in S}N(x)\) and \(N[S]=\bigcup_{x \in S} N[x]\). A subset \(X\) of the vertex set of \(G\) is called irredundant (or open-open irredundant, or closed-open irredundant, or open-closed irredundant), if for every \(x \in X\) we have \(N[x]-N \bigl[ X-\{x\} \bigr] \neq \varnothing\) (or \(N(x)-N \bigl(X-\{x\} \bigr) \neq \varnothing\), or \(N[x]- N \bigl( X-\{x\} \bigr) \neq \varnothing\), or \(N(x)-N \bigl[ X-\{x\} \bigr] \neq \varnothing\), respectively). The maximum cardinalities of an irredundant set, an open-open irredundant set, a closed-open irredundant set, an open-closed irredundant set are denoted by \(\text{IR}(G)\), \(\text{OOIR}(G)\), \(\text{COIR}(G)\), \(\text{OCIR}(G)\), respectively. These numbers are studied for circular arc graphs; a circular arc graph is a graph whose vertices can be represented by arcs of a circle, two vertices being adjacent if and only if the corresponding arcs have a nonempty intersection.