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The Cauchy problem for a nonlinear generalized pseudoparabolic equation is investigated. The well-posedness of local strong solutions for the problem is established in the Sobolev space 𝐶([0,𝑇);𝐻𝑠⋂𝐶(𝑅))1([0,𝑇);𝐻𝑠−1(𝑅)) with 𝑠>3/2, while the existence of local weak solutions is proved in the space 𝐻𝑠(𝑅) with 1≤𝑠≤3/2. Further, under certain assumptions of the nonlinear terms in the equation, it is shown that there exists a unique global strong solution to the problem in the space 𝐶([0,∞);𝐻𝑠⋂𝐶(𝑅))1([0,∞);𝐻𝑠−1(𝑅)) with 𝑠≥2.