  This paper investigates the probability density function ($pdf$) of the
$(2n-1)$-vector $(n\geq 1)$ of both lower and upper record values for a
sequence of independent random variables with common $pdf f$ defined on the
same probability space, provided that the lower and upper record times are
finite up to $n$. A lot is known about the lower or the upper record values
when they are studied separately. When put together, the challenges are a far
bigger complicated. The rare results in the literature still present important
flaws. This paper begins a new and complete investigation with a few number of
records: 2 and 3. Lessons from these simple cases will allow addressing the
general formulation of simultaneous joint lower-upper records.
