We study the cumulative quasicontinuity from above (below) of multivalued mappings of two variables.We study the cumulative quasicontinuity from above (below) of multivalued mappings of two variables. We transfer some results on the cumulative quasicontinuity of functions of two variables to the case of multivalued mappings. To do this, we first introduce the concept of weak horizontal quasicontinuity from above (below). With the help of this concept, sufficient conditions are established under which a multivalued mapping of two variables is cumulatively quasicontinuous. In particular, it is established that if $X$ is a Berean space, the space $Y$ has a countable pseudobase, $Z$ is a regular space, and the multivalued mapping $F:X\times Y \to Z$ is weakly horizontally quasicontinuous above and below and quasicontinuous below with respect to the second variable for values ​​of the first variable from some residual set in $X$, then $F$ is a jointly quasicontinuous below mapping. A similar result is established for joint quasicontinuity above: if $X$ is a Berean space, the space $Y$ has a countable pseudobase, $Z$ is a normal space, and $F:X \times Y\to Z$ is a closed-valued mapping that is horizontally quasicontinuous above and below and quasicontinuous above with respect to the second variable for values ​​of the first variable from some residual set in $X$, then $F$ is a jointly quasicontinuous above mapping. Also, necessary and sufficient conditions are obtained for a multivalued mapping of two variables to be collectively quasicontinuous from above (from below). In particular, it is established that if $X$ is a Berean space, the space $Y$ satisfies the second countability axiom, and $Z$ is a metrizable separable space, then a compact multivalued mapping $F: X\times Y \to Z$ is collectively quasicontinuous from above and below if and only if $F$ is weakly horizontally quasicontinuous from above and below and $F^x$ is quasicontinuous from above and below for all $x$ from some residual set in $X$.

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