The mixed problem for one nonlinear ultraparabolic equation the hyperbolic part of which can degenerate is considered in a bounded domain Q⊂ℝn+2" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">Q⊂Rn+2�⊂ℝ�+2. The solvability of this problem in the generalized Sobolev spases is proved using the Galerkin method.