We prove several theorems on the existence of points of symmetric "weak"continuity on the verticals for mappings of two variables. In particular, we prove the following statement. Let $X$ be a topological space with countable pseudo-base, $Y$ a Baire space with countable pseudo-base, $Z$   a metric space and $f: X × Y → Z$ a cliquish mapping with respect to the first variable and quasicontinuous with respect to the second variable. Then there exists a residual set $A$ in $X$ such that the function $f$ is symmetrically quasicontinuous with respect to $x$ at each point of the set $A × Y.$

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