  We investigate a technique to transform a linear two-parameter eigenvalue
problem, into a nonlinear eigenvalue problem (NEP). The transformation stems
from an elimination of one of the equations in the two-parameter eigenvalue
problem, by considering it as a (standard) generalized eigenvalue problem. We
characterize the equivalence between the original and the nonlinearized problem
theoretically and show how to use the transformation computationally. Special
cases of the transformation can be interpreted as a reversed companion
linearization for polynomial eigenvalue problems, as well as a reversed (less
known) linearization technique for certain algebraic eigenvalue problems with
square-root terms. Moreover, by exploiting the structure of the NEP we present
algorithm specializations for NEP methods, although the technique also allows
general solution methods for NEPs to be directly applied. The nonlinearization
is illustrated in examples and simulations, with focus on problems where the
eliminated equation is of much smaller size than the other two-parameter
eigenvalue equation. This situation arises naturally in domain decomposition
techniques. A general error analysis is also carried out under the assumption
that a backward stable eigenvalue solver method is used to solve the eliminated
problem, leading to the conclusion that the error is benign in this situation.
